In truth, there isn't a verse that explicitly states that only scripture is to be depended on.
From the beginning, Prophets and Prophetesses were God's representatives on earth, to declare the word of God. However, since the end of period of the Judges, and the installation of Kings, the main role of Prophets were to call Israel and others to repentance.
With the coming of the Apostles, they became God's representatives as you well know (and on that basis, the Apostoilic Succession, which I do not believe in).
But lets assume that there is a succession, or the Sensationalists are correct (that God continues to give us prophets and apostles), both the speaker, and the letter, cannot contradict (Galatians 1:9, Deuteronomy 18:19-23, & Isaiah 41:21-24).
And given the reality we live in (2 Corinthians 4:4, 11:13-15, & 1 John 4:1-2), the sure way to determine truth is through the word of God.
Now there is an additional reason why scripture is only to be dependent on.
Throughout church history, there's always an attempt to undermine Christian orthodoxy, and it always begins with the attempt to discredit the Bible.
You have cults that almost always use this folllowing narrative:
1. Today's Christianity is all wrong
2. The bible has been corrupted by man (or scripture too ambiguous).
3. Sin and Hypocrisy is rife in the church today
3a. Therefore, we need a prophet to rightly interpret scripture... or
3b. Therefore, we need a new translation of scripture, to have the right knowledge of God
4. Thank God he has raised Apostle/Pastor/Prophet/Teacher: [Fill-in-the-Blank] to restore Christian truths and practices long forgotten in the church today.
We need a Prophet-type to avoid the myriad of denominations therefore?
I've already detailed how united we are as Protestants; the division between is not the same division as seen in 1 Corinthians 1. Indeed, if you look at how each major denomination came about, you will see the legitimacy behind it.
Also, divisions of that nature is bound to happen; for good or for worse. Back in your own church history, in 1099, was there not a division in your church history? Which resulted in the separation of the eastern and western church. Division, is a human inevitability
Then why was the church united since the Council of Nicea? Because the church had state power.
Now I'm not one to wave a bloody shirt, but you and I both know that no one was free to start their own church movement which is why the Gnostics, the Arians, the Cathars, etc, no longer existed in the realm of the western church. Because they were persecuted, put to death, and so fled eastward.
Moreover, the threat of damnation for leaving the church is a powerful tool. It is a tried and true means to keep members from departation cult groups.
* I should say, legitimacy in nearly each one. The Angilicans came to be for illiegitimate reason which I concede (King Henry the V just wants the right to divorce). However, others like the Methodists, came to be as there was a problem of favoritism. No one at the time was reaching out to the more wretched parts of society, and so began the movement.
And, still others, like the Baptists realized the folly of Pedo-Baptism as as
it became common to think one is saved merely because of the ordinance administered while as infants.