It's difficult to determine what range a fish has here but my guess is it's a flush a lot of the time so you just have to run the math if we can call with our draw. Checking behind the turn can't be terrible but it's probably results oriented since there's still value to be had here.

I think our hand is quite nice to check back on the flop, and it's a board texture which we may want to check back some hands like this one. If we don't check back flop I'm checking back this turn always.

Just flat and fold if you miss the flush on the river.

You're getting the right price so call turn & fold river if you miss.

Correcting my post I was under the impression this guy limp/called pre. Misread the hand. Checking the flop back looks really good here.

I flatted. River blanked out (I believe it was a 2d, no draws appeared improved). Villain shoves, hero folds and villain show KsQs.

The reason I don't check back flop here is because I think most of the time I have the best hand, but it is extremely vulnerable to a lot of non-spade turns (spades would allow me to pick up equity). I guess pot controlling isn't the worst play and I probably should have considered it. These spots are areas I've been struggling in lately where on this site in particular there is so much flatting 3 bets by fish out of position who then xr or just donk pot or close to it. rethinking I think my flop and turn play may have been too results oriented.