Rainbow Dash -- Aarakocra, Way of the Open Hand Monk, and Entertainer
All of these aspects fell into place pretty quickly. I obviously had to choose something with wings for Rainbow Dash, and Aarakocra seemed the easiest way to accomplish that.
Monk was also a simple logical leap -- she moves quickly and dexterously, Flurry of Blows is practically already in her arsenal. I selected Way of the Open Hand because she's so awesome she doesn't need weapons -- she's a lethal weapon in her own right!
Entertainer is, of course, because she's a massive showboat. I considered Knight, on the grounds that she's a Wonderbolt, but frankly, they're practically all Entertainers themselves.