Its difficult (answering orig question) without more info about the betting but...
Lets assume he has launched all his chips in when he sees the flop :-
In its rawest form you could say you have 4 outs (the 4 kings). Which is 16.5% chance of hitting from the flop. You should inflate that slightly for the backdoor flush, and say give it around 20%.
Lets say he is fairly tight, maybe getting a little short-stacked though....we generously give him the following
hands :-
AA ..... 21.5% (KKKK)
KK ..... 24% (AAA and KK)
AQ ..... 21.5% (KKKK)
AJ ...... 21.5% (KKKK)
KQo ..... 28% (AAA and KKK)
KQ spades ..... 22% (AAA and KKK but no spade alongside)
QJ ..... 22% (KKKK)
We leave out the sets (unless he is incredibly shortstacked, and even then they would trade off against a complete
bluff).
Essentially you dont really want to call more than 20% ( ie no more than a bet a third of the pot size). Not exactly that attractive.
If he isnt all-in, that is a slightly different ball game once again as we need to factor in the implied odds he will bet again (in relation to his stack left and previous play) vs the implied odds of getting the pay off if you nail the turn. If you are tight then you add more weight to the implied odds he will bet again, thus reducing the draw% from the flop accordingly.
Welly