If flour seems to be accepted as sin offering/atonement, then why is blood needed?

The confusion here probably comes a likely misunderstanding of Hebrews 9:22. God does not require blood to forgive sin; this verse is more likely dealing with the initiation of the covenant. So, Jesus'death is not equitable to a sin offering, which were only for unintentional sins anyway, as I understand it. Instead, just as Moses offered the blood of an animal to initiate God's covenant with Israel as they were bought out of slavery to Egypt, Jesus offered his own blood to initiate his new, perfect covenant to buy us out of slavery to sin. This is more than just the forgiveness of sin, it is the mark of God's ownership of us so that we are no longer under the power of sin and death.

This is also why Jesus says to drink his blood and eat his flesh, even though Israel was commanded not to so because life is in the blood. Though he is speaking figuratively or spiritually, the point is clear that he is giving us his own life so we can become one with him. Through Jesus' sacrifice we are more than forgiven, we are set free and made co-heirs with him in a new covenant far superior to the Levitical one which only emphasized the death that sin brings with it.

Judaism deals with physical actions and their resulting physical consequences during one's physical life. The sin offerings cancel the immediate physical consequences of sin.

On a larger scale, the entire nation of Israel was chosen to set an example to the world. Whenever the country's leader and the people followed God's laws, they prospered; whenever they didn't they suffered. Most of the historical part of the Hebrew scriptures is a record of the alternating periods of physical prosperity and captivity.

Christianity expands the concept of sin and forgiveness to the spiritual realm, where it is one's thoughts that matter and where the consequences of sin extend into the afterlife.

Depending on each denomination's doctrines, for those that sin there will either be no afterlife or there will be an unpleasant afterlife. The spiritual consequence of sin is physical death, which is symbolized by the shedding of blood.

Those that have sinned are already obliged to die, so only Jesus's undeserved death can be used to pay the cost of their sin.

Offering fine flour is part of the theme in scripture regarding seeds. In short, fine flour is ground-up seed. The implication being that we, as seeds, are broken so that we are acceptable to God. The old man's nature is not acceptable to God. Rather, not until we are broken, yielded, repentant are we then acceptable.

In this particular case, it is not mixed with oil, because oil symbolizes the Holy Spirit throughout scripture.

Good starting references in scripture:

"Most assuredly, I say to you, unless a grain of wheat falls into the ground and dies, it remains alone; but if it dies, it produces much grain.", Jn 12:24

and, we are all seeds, too:

"But God gives it a body as He pleases, and to each seed its own body.", 1 Cor 15:38

Then, the grain offering itself - which is always fine-ground flour:

"Now this is the law of the grain offering: Aaron’s sons shall present it before the LORD in front of the altar. The priest is to remove a handful of fine flour and olive oil, together with all the frankincense from the grain offering, and burn the memorial portion on the altar as a pleasing aroma to the LORD.", Lev 6:14-15

other references to the grain offering all say fine flour. To make fine flour out of grain, which is a seed, you have to crush it and grind it thoroughly.

The analogy is we must have the old nature crushed, killed off,

"We are those who have died to sin;", Rom 6:2

and, many more.

Since the Holy Spirit cannot abide in the presence of un-atoned for sin, oil is not mixed with this fine flour sin offering.

If a person cannot afford a blood offering, God still accepts a repentant heart. Thus, the fine flour offering is acceptable. The implication being God offers forgivenness, atonement not based on our ability, but on the condition of a repentant heart, e.g.

"“These are the ones I look on with favor: those who are humble and contrite in spirit, and who tremble at my word.", Isa 66:2

17 For a testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth. 18 Whereupon neither the first testament was dedicated without blood. 19 For when Moses had spoken every precept to all the people according to the law, he took the blood of calves and of goats, with water, and scarlet wool, and hyssop, and sprinkled both the book, and all the people, 20 Saying, This is the blood of the testament which God hath enjoined unto you. 21 Moreover he sprinkled with blood both the tabernacle, and all the vessels of the ministry. 22 And almost all things are by the law purged with blood; and without shedding of blood is no remission. 23 It was therefore necessary that the patterns of things in the heavens should be purified with these; but the heavenly things themselves with better sacrifices than these. Hebrews 9

The flour offering is an exception. God showed His great mercy to the dirt poor. But to be able to offer the flour, the altar had to be first purified and sanctified. With what? Blood. And it was then annually repurified by blood again on Yom Kippur. So when one came to offer his/hers flour, the blood was already on the altar.

14 And he brought the bullock for the sin offering: and Aaron and his sons laid their hands upon the head of the bullock for the sin offering. 15 And he slew it; and Moses took the blood, and put it upon the horns of the altar round about with his finger, and purified the altar, and poured the blood at the bottom of the altar, and sanctified it, to make reconciliation upon it. Leviticus 8

15 Then shall he kill the goat of the sin offering, that is for the people, and bring his blood within the vail, and do with that blood as he did with the blood of the bullock, and sprinkle it upon the mercy seat, and before the mercy seat: 16 And he shall make an atonement for the holy place, because of the uncleanness of the children of Israel, and because of their transgressions in all their sins: and so shall he do for the tabernacle of the congregation, that remaineth among them in the midst of their uncleanness. 17 And there shall be no man in the tabernacle of the congregation when he goeth in to make an atonement in the holy place, until he come out, and have made an atonement for himself, and for his household, and for all the congregation of Israel. 18 And he shall go out unto the altar that is before the LORD, and make an atonement for it; and shall take of the blood of the bullock, and of the blood of the goat, and put it upon the horns of the altar round about. 19 And he shall sprinkle of the blood upon it with his finger seven times, and cleanse it, and hallow it from the uncleanness of the children of Israel. Leviticus 16

The altar, the animals, the blood, the tenth part of an epha (one omer) of fine flour... the whole sacrificial system were physical shadows and pictures of spiritual things in Christ. ”Without shedding of blood is no remission”. Just like the author of Hebrews says.

OP: If flour can be accepted [as a sin offering], why did Jesus have to die [atoning with blood] for the wicked?

There are a number of quantitative problems.

The sin offering of flour only was designed for and would have only covered the very poor. Christ, however, died for the sins of all (Rom 14:9).

In addition to the sin offering, there's the burnt offering, grain offering, burnt offering, ordination offering, and peace offering (Lev 7:37). Flour alone would not suffice for the list of required offerings. Christ's offering covered it all.

There's also the qualitative differences.

The flour offering had to be repeated for each incidence. Christ died once forever.

The Levitical priests offered blood not their own. Christ offered His own.

The annual atonement was also repeated, showing that sins were only covered, not fully forgiven. Christ's offering was done once to permanently pay for our sins as far as the east is from the west (Ps 103:12).

So, to answer the OP, the flour offering was limited, temporary, restricted; it only "worked" for maybe a day or two. Christ's offering covered it all forever.

The idea that "without shedding of blood there is no remission from sin" is a Christian concept expressed in Hebrews 9:22.

According to the law almost all things are purified with blood, and without shedding of blood there is no remission.

Traditional Christian theology teaches that "all have sinned and fall short of the glory of God." (Romans 3:23) Sin brought death into the world, and God sent Jesus to die so that people can be reborn into eternal life. Since "the is no remission without the shedding of blood," Jesus became a the sacrificial lamb for the sins of all humankind.

However, Jews do not share the attitude that blood must be shed for a person to be forgiven of sin. The OP rightly cites Leviticus 5:11‭-‬13 as one example. It should also be noted that in Leviticus 6, the person also had to make restitution to the one who had been wronged. The Christian sense of atonement has more to do with the concept of original sin, which brought death into the world, rather than specific sins against other people. Another example is found in Leviticus 16, where the scapegoat is offered as a living offering:

The goat on which the lot fell to be the scapegoat shall be presented alive before the Lord, to make atonement upon it, and to let it go as the scapegoat into the wilderness... The goat shall bear on itself all their iniquities to an uninhabited land; and he shall release the goat in the wilderness.

Even in the New Testament, the ritual of purification performed by John the Baptist was characterized in the gospels as a means of obtaining remission from sin with no bloodshed:

John came baptizing in the wilderness and preaching a baptism of repentance for the remission of sins. (Mark 1:4, Luke 3:3)

More important for Jews, since the Temple was destroyed in 70 c.e., Jews have not ben able to avail themselves of receiving God's forgiveness through sacrificial offerings. Prayer and repentance are now seen as sufficient, even without making offerings in the Temple. The holiday of Yom Kippur is especially significant in this context:

According to tradition, prayer and fasting on Yom Kippur will provide forgiveness for those offenses committed against God, [but] not against other people. ...Yom Kippur is a day of repentance and reconciliation for Jews and is held on the tenth day of the tenth month in the Jewish calendar—in September or October. The ten days leading up to Yom Kippur are called the Ten Days of Repentance, and during this time Jews are encouraged to seek out anyone they might have offended and to sincerely request forgiveness. ( from "the Jewish Concept of Sin")

Ultimately the issue boils down to a matter of doctrine. Christians believe that shedding blood is necessary for the remission of sins. Jews do not.

Turtledoves, pigeons, or flour are only conditionally acceptable:

⁷ “But if he cannot afford a lamb, then he shall bring to the LORD as his compensation for the sin that he has committed two turtledoves or two pigeons, one for a sin offering and the other for a burnt offering.

¹¹ “But if he cannot afford two turtledoves or two pigeons, then he shall bring as his offering for the sin that he has committed a tenth of an ephah of fine flour for a sin offering. He shall put no oil on it and shall put no frankincense on it, for it is a sin offering.

Lesser sacrifices, like flour are acceptable only if one cannot afford the other. Since God can meet any requirement, for Him flour would not be an acceptable offering.

The principle which considers a lesser offering acceptable works in the other direction as well. Since God owns it all, a lamb fails as a true value offering.

God's best is Himself in accordance with the principle given in Leviticus.

To quote from Dr Brown's Answering Jewish Objections book series:

CLAIM: Orthodox Jewish interpreters often argue that the NT authors often overemphasize the importance of blood sacrifices in the OT. In particular, the author of Hebrews writes, “Without shedding of blood there is no forgiveness” (Heb. 9:22). Is this true, or does the OT offer other means of forgiveness besides blood sacrifice?

RESPONSE: Blood sacrifices were central to religious worship in the book of Genesis (e.g. Abel, Noah, Abraham, Jacob). In the book of Exodus, the center of the Passover was a blood sacrifice (Ex. 12:13), and Moses later ratified the covenant by sprinkling blood on the people (Ex. 24:5-8). Moreover, the first reference to annual atonement in the Bible mentions the necessity of blood—not prayer or repentance or good deeds (Ex. 30:10).
ARGUMENT #3: Psalm 141:2 states that PRAYER replaces blood sacrifices.

RESPONSE: David writes, “May my prayer be counted as incense before You; the lifting up of my hands as the evening offering” (Ps. 141:2). However, this statement does not replace blood atonement. David is merely making an analogy regarding his prayer life—not a complete overhaul of blood atonement sacrifices. The original meaning had nothing to do with replacing blood sacrifice with prayer.

ARGUMENT #4: Leviticus 5:11-13 states that FLOUR replaces blood sacrifices.

RESPONSE: Verse 12 explains that the flour was added to the blood already on the altar. Moreover Brown writes, “Nowhere is it written that ‘the flour will make atonement’ or that ‘the life of a creature is in the flour.’ Rather, the whole basis for atonement was in the sacrificial blood on the altar, and through a flour offering, even poor Israelites could participate in the atoning power of the altar.”

Also read detailed quotes and explanations from the Jewish sources refuting the Jewish modern objection against the whole sacrificial system, here on biblestudying.net. Moreover, note that the red wine at the Passover Seder symbolizes blood:

This point about the slaughtered children is also mentioned in the Ohr Zaruah, Vol. II, Siman 256 (Left column, bottom quarter) and he adds two other symbolic cases of blood. He writes:

יין אדום זכר לדבר שהיה פרעה שוחט תינוקות כשנצטרע ועוד זכר לדם פסח ולדם מילה

Red wine as a remembrance for Pharoah who slaughtered the babies (and bathed in their blood) when he was suffering with leprosy. And furthermore, it is a remembrance for the blood of the Korban Pesach (the Paschal Lamb) and the blood of milah (circumcision).

Blood, flour, or whatever was offered in the temple didn't "actually" take away sin. It was faith directed toward God in participation of the process that God had instituted which covered sin until the promised One had come.

The process is no longer faithful temple worship. The process is now belief in the Son of God unto new birth. It has always and only ever been the shed blood of Jesus Christ which takes away sin. Before He came and died it was faith in the promise and now it is faith in the actuality.

Jesus, the Lamb of God, shed his blood at a specific temporal point on earth but, in God's eternal economy the Lamb was slain from the foundation of the world. All of the forgiveness available through repentance, prayer, temple ritual, etc. is based upon the shed blood of the Son of God.

The next day John seeth Jesus coming unto him, and saith, Behold the Lamb of God, which taketh away the sin of the world. - John 1:29

And as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up: That whosoever believeth in him should not perish, but have eternal life. - John 3:14-15

From a Christian viewpoint, the Jewish sacrificial system was a metaphor pointing to Christ's sacrifice as the ultimate fulfilment. The concessions concerning what was acceptable to offer in sacrifice were to not place an undue burden on the poor. No sacrifice made by people, whether of rams or goats or grain, removed the necessity of Christ dying for our sins. They just pointed to it.

Each of the Levitical sacrifices tells part of the story of redemption, not the whole.

The necessity of Christ's sacrifice and the inadequacy of all others is expressed in Hebrews 10:1-7:

The law is only a shadow of the good things that are coming—not the realities themselves. For this reason it can never, by the same sacrifices repeated endlessly year after year, make perfect those who draw near to worship. 2 Otherwise, would they not have stopped being offered? For the worshipers would have been cleansed once for all, and would no longer have felt guilty for their sins. 3 But those sacrifices are an annual reminder of sins. 4 It is impossible for the blood of bulls and goats to take away sins.

5 Therefore, when Christ came into the world, he said:

“Sacrifice and offering you did not desire, but a body you prepared for me; 6 with burnt offerings and sin offerings you were not pleased. 7 Then I said, ‘Here I am—it is written about me in the scroll— I have come to do your will, my God.’ "

A New Covenant

Part of the confusion seems to stem from the covenantal nature of the sacrificial system. The offer to forgive sins if the ritual sacrifices were performed was contingent upon keeping the first covenant, made in the time of Moses. That covenant was broken, so that promise was voided. The basis for forgiveness is now the new covenant in Christ's blood.

“The days are coming,” declares the Lord,
    “when I will make a new covenant
with the people of Israel
    and with the people of Judah.
32 It will not be like the covenant
    I made with their ancestors
when I took them by the hand
    to lead them out of Egypt,
because they broke my covenant,
    though I was a husband to them,”
declares the Lord.
33 “This is the covenant I will make with the people of Israel
    after that time,” declares the Lord.
“I will put my law in their minds
    and write it on their hearts.
I will be their God,
    and they will be my people.
34 No longer will they teach their neighbor,
    or say to one another, ‘Know the Lord,’
because they will all know me,
    from the least of them to the greatest,”
declares the Lord.
“For I will forgive their wickedness
    and will remember their sins no more.” (Jeremiah 31:31-34)

Here is where Jesus proclaimed the new covenant:

26 While they were eating, Jesus took bread, and when he had given thanks, he broke it and gave it to his disciples, saying, “Take and eat; this is my body.”

27 Then he took a cup, and when he had given thanks, he gave it to them, saying, “Drink from it, all of you. 28 This is my blood of the covenant, which is poured out for many for the forgiveness of sins. 29 I tell you, I will not drink from this fruit of the vine from now on until that day when I drink it new with you in my Father’s kingdom.” (Matthew 26:26-27)