bet/folding seems bad assuming BTN will always raise your cbet with KK, although b/3betting also seems marginal at best vs BTN. I think check/shove is going to be even worse than b/3bet because BTN may find a fold with KK if UTG also calls
so i think c/c flop is best because there are only six turn cards I can think of that are definitely folds (non spade K/T) and this is our best line to induce a bluff, tho that also seems improbable