While we must always be careful with apocalyptic language - and I may well be guilty of being too literal where I should not be - Peter's understanding that the heavens and earth would be devoured by fire need not be negated by the heaven and earth fleeing in Rev 20:11. This verse is in reference to the Lord's return to judge the earth. That judgment must happen in the presence of those who are to be judged (the sea - which has no place in the new [21:1] gives up the dead in it).
The new heavens and new earth of 21:1f are post judgment, they are the eternal home of the eternal family. By this stage the first heaven and first earth had not simply 'fled' but 'was no more' (ouk estin eti - no longer is). The destruction of the old 'by fire' occurs between the judgement of those of the old, bringing this age to and end, and the appearance of the new and eternal.
Peter's understanding that the earth would be destroyed by fire may have come from the many useages through the Scriptures as fire as a means or expression of God's judgment. It may be a contrast to the destruction of the flood. It may be an extension of the use of fire in judgment in teh Revelation (e.g. 20:9). But it may also be something he/they had been taught directly from Jesus.
As for 1 Peter being after the Revelation, I think (and have produced an historical reconstruction to support) that the only books written prior to the Apocalypse were Galatians, 1&2 Thess, 1&2 Cor, Romans, Philippians and Hebrews. The last two of these especially were, I believe, written soon before and into the situation that the Revelation was given. Apart from John, Matthew, Luke and 2&3 John, I think the rest of the books were written in the two years following the Revelation (mid 62) and before Nero's persecution commenced (late 64). They were all written with the Revelation in mind and were part of the apostles' preparation of the Church for the final tribulation they thought would preceded the return of Christ.