Hi, Im giving you my feedback without reading other peoples responses
I think your preflop and flop bet were fine. Without a read on the remaining villain its a bit complicated. I'd assume had you been facing AA-KK-AK you would have been reraised preflop. AQ is a possibility here, but even with the flush draw present you had to bet. Your flop bet is giving him a little over 2 to 1 odds
to draw to his flush so if he calls, hes making a mistake.
Now on the turn, the only hand the ace completes is the AK-AQ, possibly at this stake people call raises with any ace, I dont see too many 2-pair combos, so I personally wouldnt shut down here. If you check, he might interpret your hand as weak or scared of the ace and barrel the turn, or value bet a worse hand like 88-JJ so a check call is an option to not get bluffed off your hand.
I personally dont mind leading out here either, but its difficult with no read on the guy. But I wouldnt want a calling station to get a free flush card on the turn, hence my betting at least 3/4 pot on the turn would be my first option.
I feel that if the river is a non scare card, your hand becomes a good bluff catcher. You can check call a decent sized river bet but if he pots it or shoves with the third flush card, then you have a more difficult decision, hence why reads on the guy even if its s superficial one like '' generally tight or loose'' helps you out with your decision here.