You can also make a small bet, a very small bet, lets day 40$. Maybe villian can think he can bluff you if he has nothing. If he has the Ah he will surely shove, and if he has a weak flush he will call for odds
, while if you push you only get called by Ah and maybe Kh, in this way you make room for bluffs, Ah shoving, Kh possibly shoving, and you get small value from weak flushes that will never call you shove, and will check behind if you check
Information about villian is needed in order to be able to conclude on the best play, remember you have to play the man not the game.