I'll put it bluntly, you shouldn't lay this down. Especially with 4 to a flush on the board, if someone has the K (and possibly the Q or J) they play pretty much the same way. You can kind of take the possibility of trips away because they would be raising afraid of the flush draw, and when the fourth spade came they wouldn't have re-raised. So you figure they have one of 3 hands: a good flush, the boat that he had, or quads. Quads and boat fit in the same category, but are both very very very rare. You didn't post bet sizes but I'm assuming you were getting decent odds
and you have the nut flush. No way you can fold. Just know that in the other position, you double up or stack your opponent too.