I agree with the previously poster, only way here I'd consider slowplaying set here is when villain is aggro aggro as hell, you have to be sure he'll smash this ace high board to check here or you always losing value/risking getting drawn over without punishing the opponents.

Bet small flop, around 40%-50%, they prob won't be going ahead in this board since you already take 2 out of the 3 aces there are, only drawing hands mostly you will be taking here given your hand.

If villain pays/2 villains pay and turn is blank I suggest you put higher price there, as things can get ugly

would you all check turn on a flush card ?

The problem with that, imo, is that our range is face up when we do that and we are exploitable vs a good player. Maybe its not that big of a deal at 10nl, but by checking OTT, we would bet only with flushes (and bluffs to balance) and check all other good hands (with intention of folding at some point if vilain bet turn bet river ?!). This is too easy to play against. If we want to add strenght to our turn checking range on a flush card, we would need to start adding flushes in the range and I think we lost value.

Im just not sure if its better to bet (it would be a shove) ourself OTT and hope to get value vs lower set and TP TK/good kicker ..

WHAT?? "intention of folding at some point if vilain bet turn bet river" We're checking behind turn, so if he bets river a reasonable size I call. If he pops it I evaluate his tendencies and his whole range on that river card, but probably call most of the time.

I would check turn to pot control.

you cant pot control as the next bet is probably AI given the stack size and the size of the pot. I dont think vilain will shove turn with a lot of worse hands, but I think he is more likely to call your shove with worse.

Ok, what Im gonna say is theoretical and assume that there is more money behing. Lets say there is enough money left for 2 more bets, that means you are checking the turn, but x/c turn and river if he bets ?? Since your range is face up as TPTK-set (because you bet the top of your range in this spot) , vilain can play you perfectly and only bet the top of his range. In that case, you should start to adjust and fold all your range vs his bet because you're never good. But again, vilain will adjust and start bluffing (because you always fold)and you'll start calling again (with him readjusting and betting only better hand). That why I said that if you have a checking range, it shouldnt be capped, but should include some flushes. The problem with that is the few flushes combos in your range probably doesnt allow you to have some combo in your turn betting range and have enough in your turn checking range.

All that being said, I think I'd have all those hands in my betting range and no continuation turn checking range at all.

Next bet is push if you cbet flop that big, if you cbet smaller, you can play 3 streets.

I agree with cpau I would also barrel most diamond turns against most unknown villains but I dont really fault a check for pot control, but i think betting is just better for reasons he said+ if you villain has like KJ with a diamonds or QJ with a diamond, KK with a diamond, hands like that, You dont really wanna give a free card to those hands. In the case your villain has a flush you can still boat up.
If you have reads villain check raises turn alot then I would lean towards a check however, getting raised on a diamond turn is a really tough spot.

OK. We have position so is check-behind, and always calling river. So if you're concerned you always do that with your weaker range, you can do the same with your strong range. :)

if flush comes on turn isnt more balance to bet anything we lead flop with...??? i feel like im gonna get called more when i have the nuts and i will maybe force opponent to do mistake when i have a set or 2 pair

You're right, I thought we had position. Still I would XC with flushes to protect my weaker range to balance. I can XC turn and probably XF a blank OTR.

But against this villain, I would XC turn and river if he is agro++

esso.g - that's exactly what I tried to explain in my long post. I feel like betting my entire range OTT is better than splitting it into a xc range and a betting range. There is more value in betting imo..At these limits, people are more likely to make a mistake by calling too much than by betting too much so the value is greater than usual when you valuebet your good hands.

Your thought process make sens, but depending on the situation (this one is 3way with a 3bet cold caller preflop), vilain isnt gonna have that many flushes in is range after calling the 3bet pre once the board has the A of the flush. I dont see him having hands like QTs/JTs or even KT... I'd say the Ad here remove a lot of flushes combo, so KQs is definetely in his range, maybe KJs, but what else (after calling a 3bet preflop) ?

I think our range is just way ahead of him and its another reason why I prefere having a betting range OTT instead of a checking range.