flushy flop, EP

This is a general question about a type of situation that I am sure we have all found ourselves in, and I'd be interested to hear people's thoughts. It is when we are in early position having called a raise (say 1/5 our stack) and have hit the flop hard, but there is a made flush available but not to us.

E.g: we hold AdKh in BB and have called a substantial raise PF. The flop comes QsJsTs and we are first to act. How to proceed?

My instinct is to donk bet hoping the villain will fold and then abandon the hand if I get action but I am not sure this is the best way forward. Although we have a straight it seems as if any play is basically a bluff and with no way of improving all we can hope for if we are to win is that the villain fails to make a flush draw, but this could be expensive if we bet each street.

Any ideas?

check, if you get raised, call, then bet on the turn

If I had AK in the BB, I would have pushed PF if his raise was 1/5 my stack, but I don't think that's your question. Hopefully you have some reads on this guy, like everything else in poker it depends. If the guy was playing tight I might push on him, thinking he raised with an Ax or pair. If he has one spade in his hand you want to put the pressure on him and not just check it to him. What if he min bets? You'll call. Then another spade hits.What then? You just called off almost 1/2 your stack. When you're that low you gotta get it in fast with AK.