[Ghazban]

You should also come to the conclusion that the flush draw would maximize his EV by pushing the flop even if he knows he's up against two aces. Your original phrasing of the scenario was somewhat paradoxical as the flush draw player would not check that flop (even if he knew he was against aces), particularly if he understood pot odds as you stated he did. The whole issue of what the AA should do is mostly irrelevant as the AK should never have checked in the first place.