Only reason I can come up with for B/F OTF here: I am not interested in spiking a king OTT, because I'll fold to a check/raise OTF & shut-down OTT when he just calls my flop bet & V checks Turn & let V take down pot with a River bet, unless I spike a king, or his bet OTR is too tempting & I let him make some more money when he has an ace.
Checking seems good because it keeps villain and your range a little wider, there's really no bad cards for you on the turn so you're not worried about protection or equity denial.
Flop bet makes for an easier showdown in this game and there's value to be had considering how often pairs will peel once. Beyond that you're probably just bluffing.