I only got one 'general' tip. Works for everything:
Draven is a champ that needs to warm up first - 1 Q, wait 6-9 secs (depending on level). Q again (2 axes up). Then just waiting till Q's cooldown (while still having those 2 axes up). So, basically, you got 3 axes up and running. And try to keep em like that, watch the buff times, hit anything that might refresh it. (don't forget your red).
While 3 axes up:
The tricky part is achieving this, however, if you do duel in this manner against any squishy champ, you will likely rekt em. Do not only use E for escaping, use it also offensively. Dont just ult a fleeing target, also do it like/as an engage aperture if there is more than 1 foe in front of you. Flash+E to sides if enemy is a CC mage (ie. lissandra). Juke with your W (skill shots, aoe ults, etc).
You can play with everything i mentioned (i.e. Ult + flash + E, Q, W, Q, etc) Think fast, try to keep up with Draven. Hes currently STILL, the best ADC out there. Not even LeBrown can match him.