I've never liked trading up and mortgaging future draft picks. The player you're trading up for better be a stud if you invest so much in him. I've always preferred BPA, or if the value isn't there, trading down for more value. The Patriots do it well almost every damn year. As long as you hit on the majority of your extra picks, it is a strategy that is hard to beat.
I'm willing to bet this new regime will covet all of their picks and hope to build a team more in line with their philosophies. It's hard to put a stamp on a team with just one player, even if it is a possible franchise qb. The ideal situation for Miami would be to acquire your possible franchise qb through free agency (likely Flynn or Manning) and use your draft picks to shore up whatever the front office then presumes to be our greatest needs or BPA.
If Miami misses on Flynn and Manning, or doesn't want them, then the scenario of moving up for RGIII becomes more plausible, but no less expensive. I would still say Miami should hope RGIII falls a few spots and then attempts a trade up, or waits until next year for their franchise qb while addressing other key positions while rolling with Matt Moore or whomever then is affordable at qb. I'm sure Miami's new staff is already under great pressure to come out strong, but a losing season with Moore or someone else at qb next year would be tolerable as long as Miami hits on other players in this year's draft.
If I had to guess right now, I'd say we go after Manning, then failing that, go after Flynn. I bet we take BPA at 8 or 9 (whoever wins the coin toss).