AA32ds flopped nutflush

Your flop bet is way too strong, you can get away with betting 80 cents on the flop to balance your bluffs and also to give villain a reason to call with hands that are drawing thin.

After you bet so strong on the flop I think you have to check back this turn card. Villain sometimes has a worse flush and if he does he is folding the turn pretty much always since too many hands are now beating him. If you check the turn you can still fire the river if villain checks again to get value off worse flushes (since if you bet the turn and get called you're checking back 90% of rivers anyway).

On the river it's hard to see how you can get value now. Maybe Q or J high club flush just backdoored in to QQ or JJ full house but at the same time he could be slow playing KK on the turn and is now scared of quads.

I think you need to look like this river is a bit bluffy so you can probably get away with hitting the bet pot button and folding to a shove (even KK isn't checkraising to a full pot bet) since it's always quads. If villain does have QQ or JJ he probably makes a hero call irrespective of how much you bet the river.

My only worry is that your strong flop bet isolated yourself against sets and worse flushes and there isn't a whole lot you can get paid off by on the river since 44 has to fold.

You got the hand wrong. I didn't bet the flop. SB donkbets.

Definitely raise the flop then, a turn card could kill all the action if it pairs the board. donk bets are typically weighted towards complete bluffs, 2 pair, sets and also weak flushes. If he is bluffing he will give up once you call the flop so what you care about is winning more money against the rest of his range.

Think about how you would play the hand if you had a naked ace of clubs and play it the same way. (by raising big on the flop most likely)