Where does it claim final authority?
Matt 24:35, Acts 17:2, Acts 17:11, 1 Thess. 2:13, 2 Tim. 3:16 for starters. Think about it. What would the final authority be below God if not His Word? If scripture is truly inspired by God, then it must by definition be the final authority and no one below can contradict it. Appeals to scripture are final appeals. Take the whole book of Hebrews as an example.
Now you know none of those Scriptures say any such thing, or you wouldn't be telling me to "think about it" : you'd be quoting.
What would the final authority be below God if not His Word?
The guy he gave the keys to the kingdom, and his successors.
If scripture is truly inspired by God, then it must by definition be the final authority and no one below can contradict it.
No, it must by definition be "correct." Scripture can not be the final authority if it makes no such claim.