How does one obtain such a valuable asset?
(1) Own a very high draft pick (perhaps # 1-3) in a year when an "can't miss" QB is available. In my lifetime, only two "can't miss" college QBs have proven to be elite (John Elway and Peyton Manning). The road is littered with failures. The current "can't miss" college QB, Andrew Luck, will be snapped up very quickly. Robert Griffin III is generally highly regarded but is not a guarantee to succeed. Cam Newton had many detractors last year but has proven to be elite. A team can certainly try to trade up to acquire a higher draft pick, at massive cost. Why not just set sight on someone and do this? Because a failure could set a franchise back 5-10 years or more. The Giants succeeded by trading for Eli Manning but there are no guarantees. The odds are not good.
(2) Try to obtain an elite QB by trade or waiver. This is pure fantasy. Elite QBs are treated like rare gems, never to be surrendered under any circumstance. Did everyone notice how the Steelers came to Ben Roethlisberger's defense when he had his legal troubles last year? The Steelers hadn't had an elite (or even a decent) QB since Terry Bradshaw in the 1970's. They weren't about to let Roethlisberger get away.
(3) Free agency. See #2 above. Elite QBs are never permitted to just "walk away" so this is likewise a pipe dream. It is possible Matt Flynn may grow into an elite QB but this is still debatable. The only examples I can think of are Kurt Warner, signed from Arena Football, and Johnny Unitas back in the day. Joe Theisman was an excellent QB, a Super Bowl winner, but wasn't elite.
(4) Serendipity. This is how the vast majority of elite QBs have been obtained in the past. Tom Brady? 6th round draft pick. Joe Montana? 3rd rounder. Dan Fouts? 3rd rounder. Roger Staubach? 10th rounder. Brett Favre? 2nd rounder. Bart Starr? 17th rounder. The sainted Dan Marino? Last pick of 1st round. You get the idea. The Dolphins had Hall-of-Fame QBs from 1967-2000 (except for Woodstrock 1980-1983). Few other NFL teams had such a long run with elite QBs but things have certainly evened out over the last decade.
My advice? Philbin should take a chance on Matt Flynn if the cost is not too great and the Dolphins aren't crippled by the move if it should fail. Otherwise, draft a promising second-tier college QB this year and coach him up. One never knows.