Hmm it's close. As they limped and are fish I would go ahead and make a small bet to charge FDs ad check decide the river.

I really don't expect them to value bet Ax on a 3 flush flop as they look passive so I'm not that worried about getting bluffed.

Think I'd usually chk this one, we're only going to be bluffing with our kings if we bet surely and most unlikely to get called by worse imo.
I suppose we could bet but if we get raised it's gonna suck so I don't like that idea either.

I think it is pretty equal when it comes to betting or checking as we have the Kc. We can check flop and value bet turns and rivers or just bet into our nut flush draw and set draw knowing villain isn't going to have many big aces in his range and liable to call down with worse.

It's really close and depends on your opponent. I don't see anything bad in firing again vs. a really loose-passive player, but I think that checking will be better vs. most players.

I would bet again and c/f river vs a passive player
vs an aggro player this is a good hand to check to balance vs floats and you can consider calling down on the river too
If you hit your flush I would bet on the bigger side

Flop: Put this hand into your check/call range.

Turn: As played, fire again as we have Kx nut blocker not scared of getting raised as we can just shove over the flop and put villian in a awful spot.

River: Overbet 2 to 3x pot on any card which does not pair the board otherwise check. We want to put maximum pressure on his weak Ax. Also, when you do make your flush mix it up between betting and checking. Your going to need some nut flushes in your checking range to protect the your sets and 2 pairs which will be check/folding river.