Some immediate concerns:
Is this really a problem that most people have? (i.e., do most people think Kayak sucks that much?)
Even if they do, how often is this a problem? Once a year?
Are you cooked if Google finally makes a decent flight search engine?
Do the most frequent/valuable flyers even care? (business flyers who aren't paying the fare anyway)
Your solution is full of friction and extremely slow (paying, waiting for results, administering a contest, etc). This model works for 99designs because hiring designers is even more annoying and unpredictable than running an auction. Is flight search the same kind of problem?
The angle, of course, is that you can "resell" the surfaced deals. i.e., when a good deal is surfaced you can promote it on your homepage, sell it to others, and hopefully make a nice commission from the airline. I get that. I just don't see enough people using the service to surface enough deals for this kind of serendipity, and there's nothing to stop Kayak/Orbitz/etc from scraping the deals you do find.
That said maybe you'll learn enough about 'why flight search sucks' that you'll invent a killer new engine and get rich. But I don't think crowdsourced deal finding for flights is a viable idea.