KK on Flush, Str8 board.

This is interesting. Would villain have led on the turn even though you made a continuation bet on the flop with AQ of clubs let alone with 27BB? I wouldn't be too concerned of the flush. I can't even think of any combination of two cards of clubs that he could have called with preflop and bet 27BB with on the turn. But, Id be concerned with AQ (16 combinations) and KQ (8 combinations); QQ (6 combinations), QJ (12 combinations) were also possible. Your bet on the turn was probably too small to discourage villain from continuing with a double gut-shot or gut-shot straight draw. I'd fold as you did too.

I don't understand your post flop play, especially the flop. You have 2nd back door fd and block some straight and only bet here almost 1/3, why? What is your plan? This flop i cbeted about 15 or 16BB. And turn maybe hit a straight or lower flush but big donkbet i think KQ or Q9, AQ, QJ. But you still count flush and higher straight and you have got position. Maybe better the fold but i think this board you can call and see the river.