The word "inspiration" is used twice in the Bible, and if you're a Bible believer like I am, you'll submit the words within the Bible to Its own definition, meaning you'll put the two verses together in context and accept that meaning as factual. Can we give that a shot?
II Timothy 3:16: All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:
Please notice, this verse most emphatically does NOT say that all scripture is inspired: it says that all scripture is GIVEN BY INSPIRATION. If you say "the Bible is inspired," you're subjecting the words of God to your own private interpretation, contrary to 2 Peter 1:20.
Job 32:8: But there is a spirit in man: and the inspiration of the Almighty giveth them understanding.
So here we have the other verse, and as anyone with a brain in their head can see, "inspiration" is dealing with supernatural involvement in human comprehension; i.e. the "Almighty" giving understanding through inspiration.
Therefore, when you combine the two verses, as true Bible believers should do, you'll see that all scripture (including the Bible that you claim to believe, if you really believe it) is given by the supernatural understanding given by God to men. As a result, scripture is not inspired: the men who write it are! Therefore, there's no such thing as "double inspiration," since the Bible was never inspired even once in the first place! God preserved His perfect words through the centuries and compiled them in the King James Bible in 1604-1611, but He never inspired them. He inspires the men that He uses to preserve and translate that Word.
Got a better explanation? Biblical, of course; I don't give two farts about any other kind.