Committing a sin by eating animal's flesh

According to the Holy Bible, are we committing a sin by eating animal's flesh?

The simple answer is no, because God made it quite clear himself.

Apparently, Adam and Eve did not eat of the flesh of animals.

29 Then God said, “I give you every seed-bearing plant on the face of the whole earth and every tree that has fruit with seed in it. They will be yours for food. 30 And to all the beasts of the earth and all the birds in the sky and all the creatures that move along the ground—everything that has the breath of life in it—I give every green plant for food.” And it was so. - Genesis 1:29-30

However things changed after the flood with Noah. After the biblical flood, God gave man permission to eat the flesh of animals.

9 And God blessed Noah and his sons, and said unto them, Be fruitful, and multiply, and replenish the earth.

2 And the fear of you and the dread of you shall be upon every beast of the earth, and upon every fowl of the air, upon all that moveth upon the earth, and upon all the fishes of the sea; into your hand are they delivered.

3 Every moving thing that liveth shall be meat for you; even as the green herb have I given you all things.

4 But flesh with the life thereof, which is the blood thereof, shall ye not eat.

5 And surely your blood of your lives will I require; at the hand of every beast will I require it, and at the hand of man; at the hand of every man's brother will I require the life of man. - Genesis 9:1-5

Let us not forget the great vision of a sheet with animals of St. Peter the Apostle, as mentioned in the Book of Acts.

4 But Peter explained it to them in order from the beginning, saying: 5 “I was in the city of Joppa praying; and in a trance I saw a vision, an object descending like a great sheet, let down from heaven by four corners; and it came to me. 6 When I observed it intently and considered, I saw four-footed animals of the earth, wild beasts, creeping things, and birds of the air. 7 And I heard a voice saying to me, ‘Rise, Peter; kill and eat.’ 8 But I said, ‘Not so, Lord! For nothing common or unclean has at any time entered my mouth.’ 9 But the voice answered me again from heaven, ‘What God has cleansed you must not call common.’ - Acts 11:4-9

As for the interpretation of this last text here is what Wikipedia has to say:

Simon J. Kistemaker suggests that the lesson God taught Peter in this vision is that "God has removed the barriers he once erected to separate his people from the surrounding nations.": 378 Kistemaker argues that it means Peter has to accept Gentile believers as full members of the Christian Church, but also that God has made all animals clean, so that "Peter with his fellow Jewish Christians can disregard the food laws that have been observed since the days of Moses.": 380 Albert Mohler, President of Southern Seminary, writes:

As the Book of Acts makes clear, Christians are not obligated to follow this holiness code. This is made clear in Peter's vision in Acts 10:15. Peter is told, 'What God has made clean, do not call common.' In other words, there is no kosher code for Christians. Christians are not concerned with eating kosher foods and avoiding all others. That part of the law is no longer binding, and Christians can enjoy shrimp and pork with no injury to conscience.

Luke Timothy Johnson and Daniel J. Harrington write that this episode heralds a radical change in Peter's "identity as a member of God's people,": 187– but also that "the implication is that all things God created are declared clean by him, and are not affected by human discriminations.": 184.

On the other hand, the United Church of God (a group following the teachings of Herbert W. Armstrong) calls this an "often-misunderstood section of the Bible", arguing that Peter's statement in verse 28 indicates that the divine disclosure reflected only a teaching about people, and not one about food. The UCG argues that Peter realised "the puzzling vision could not be annulling God’s instructions." The Seventh-day Adventist Church has a similar view of this passage. - Peter's vision of a sheet with animals

Paul deals with exactly this matter in his first epistle to the young minister, Timothy :

Now the Spirit speaketh expressly, that in the latter times some shall depart from the faith, giving heed to seducing spirits, and doctrines of devils; Speaking lies in hypocrisy; having their conscience seared with a hot iron; Forbidding to marry, and commanding to abstain from meats, which God hath created to be received with thanksgiving of them which believe and know the truth. For every creature of God is good, and nothing to be refused, if it be received with thanksgiving:

[I Timothy 4:4 KJV]

I think there is no need for me to add any further words.

I have simply highlighted what is most relevant to the question.