What is the basis for the claim that "we have the completed revelation from God in the Bible"?

What is the basis for the claim that "we have the completed revelation from God in the Bible"?

What is the purpose of the "complete revelation"? To what does the Bible point?

And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone; Eph 2:20

The church, the holy temple in the Lord (Eph 2:21) is built on the foundation of NT apostles and OT prophets.

Did God forget to provide us a "complete revelation? No.

But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name. John 20:31

For whatsoever things were written aforetime were written for our learning, that we through patience and comfort of the scriptures might have hope. Rom 15:4

These things have I written unto you that believe on the name of the Son of God; that ye may know that ye have eternal life, and that ye may believe on the name of the Son of God. 1 John 5:13

Beloved, when I gave all diligence to write unto you of the common salvation, it was needful for me to write unto you, and exhort you that ye should earnestly contend for the faith which was once delivered unto the saints. Jude 1:3

The Bible is replete with "it is written" statements that point to its complete revelation from God for all things salvific.

2 Peter 3:1-2 This second epistle, beloved, I now write unto you; in both which I stir up your pure minds by way of remembrance: That ye may be mindful of the words which were spoken before by the holy prophets, and of the commandment of us the apostles of the Lord and Saviour:

Peter wrote it down for us.

Biblically, the basis for the doctrine of "completed revelation" is the idea that John 16:13 ('He will guide you into all the truth') was already fulfilled in the Apostolic Age. Historically, it is related to the tension between church authority and spirit-led teaching outside of episcopal supervision. The charismatic offices of apostle, prophet and teacher, in which God revealed new messages and teachings directly, were subsumed under the institutional offices of bishop, presbyters and deacons. Meanwhile the biblical canon developed as a the scriptural expression of Truth.

Apostolic Fathers

The earliest manifestation of episcopal authority over prophetic charismatic activity may be the teaching of Ignatius of Antioch, who commanded: "Let no man do anything connected with the Church without the bishop." (Smyrnaeans 8)

The Didache expresses a concern that prophets may disrupt the church and do not always practice what they preach. It also states that bishops should begin to replace the role of prophets:

...not every one who speaketh in the spirit is a prophet, but he is so who hath the disposition of the Lord; by their dispositions they therefore shall be known, the false prophet and the prophet... Elect therefore, for yourselves bishops and deacons worthy of the Lord, men who are meek and not covetous, and true and approved, for they perform for you the service of prophets and teachers. (11-13)

Montanism

The issue of new revelation reached a critical point during the Montanist controversy. This "New Prophecy" involved a claim of direct revelation from the Holy Spirit to reform and revive the Church. It was eventually condemned by the bishops of Asia Minor c. 177 but not until it had become a major movement. According to its most illustrious convert, Tertullian, even the Pope initially approved of its message:

...after the Bishop of Rome had acknowledged the prophetic gifts of Montanus, Prisca, and Maximilla, and, in consequence of the acknowledgment, had bestowed his peace on the churches of Asia and Phrygia, he [the anti-Montanist teacher Praxeas], by importunately urging false accusations against the prophets themselves and their churches… compelled him [the Pope] to recall the pacific letter which he had issued, as well as to desist from his purpose of acknowledging the said gifts. By this Praxeas did a twofold service for the devil at Rome: He drove away prophecy, and he brought in heresy; he put to flight the Paraclete, and he crucified the Father. (Against Praxeas. ch. 1)

The rejection of Montanism signaled the beginning of the end of prophecy as a means of important new revelation.

Personal prophecy vs. Major New Revelation

The above developments, together with the formation of the biblical canon, formed the historical basis for the rejection of new revelation in Catholic and Orthodox tradition. However, it is not correct to say that the Roman Church rejects prophecy altogether. According to the Catholic Encyclopedia:

The last prophetic work which the Church acknowledges as Divinely inspired is the Apocalypse. The prophetic spirit did not disappear with the Apostolic times, but the Church has not pronounced any work prophetic since then, though she has canonized numberless saints who were more or less endowed with the gift of prophecy. The Church allows freedom in accepting or rejecting particular or private prophecies according to the evidence for or against them.

John 16:13 Already Fulfilled

Protestant churches have various policies regarding continuing revelation. For Pentecostal churches, prophecy is a major component of worship. Liberal Protestants and Evangelicals usually reject the idea that revelation has continued beyond the Apostolic Age. Although God does communicate personally with believers, this communication does not foretell major events or provide new information to the Church as the body of Christ. An article in the Evangelic Times expresses the basis for this attitude:

‘When the Spirit of truth comes’, said Jesus, ‘he will guide you into all the truth, for he will not speak on his own initiative, but whatever he hears he will speak; and he will disclose to you what is to come’ (John 16:13).

The great majority of Bible-believing Christians down the ages have understood this promise to refer to the inspiration of the New Testament writings – completed around A. D. 90 with the book of Revelation. There is no reason to think that this work of the Holy Spirit can be pushed beyond the Apostolic age. Paul declares that the ‘mystery of Christ … has now been revealed by the Spirit to his holy apostles and prophets’ (Ephesians 3:1-7, 9-10).

SUMMARY: The historical basis for the end of revelation emerged out of the tension between church's teaching authority and direct communication from God to prophets and teachers who saw themselves as personally called by God outside of ecclesiastical channels. The Montanist controversy marked a major milestone in this development. The biblical basis for rejecting new revelation is derived from Ephesians' teaching that the mystery of Christ was already revealed in the Apostolic Age, together with an interpretation of John 16:13 to the effect that "all the truth" refers to the biblical canon.

God has revealed everything we need to know about him, what he has done for us and what he is going to do for us, and what he expects from us, in the Bible, the written word of God. Christians understand that the revelation of Christ Jesus, given to the Apostle John, was the last revelation.

The Got Questions article you partially quote from is about people claiming they have received some new revelation from God – some prophecy or revelation that is in addition to what has already been recorded in the Bible.

Some denominations claim that in these modern times they have received special revelation from God and have recorded these things in written form. It is worth remembering that any revelation from God given after the book of Revelation was sealed would of necessity have to be in absolute agreement with everything else revealed to us in the Bible. God neither lies nor contradicts himself. That is the litmus test for any new or special revelation that men claim to have received from God.

Going back to your question which asks “What is the basis for the claim that "we have the completed revelation from God in the Bible", the answer is found in the Bible itself:

The ultimate form of special revelation is the Person of Jesus Christ. God became a human being (John 1:1, 14). Hebrews 1:1-3 summarizes it best, “In the past God spoke to our forefathers through the prophets at many times and in various ways, but in these last days he has spoken to us by his Son … The Son is the radiance of God’s glory and the exact representation of his being.”

God became a human being, in the Person of Jesus Christ, to identify with us, to set an example for us, to teach us, to reveal Himself to us, and, most importantly, to provide salvation for us by humbling Himself in death on the cross (Philippians 2:6-8). Jesus Christ is the ultimate “special revelation” from God. https://www.gotquestions.org/general-special-revelation.html

The answer to your question is simple – God used to speak through the prophets in the past, but now he has spoken to us through his Son, Christ Jesus.