i jam kq in this spot 100% of the time.
the hand is too strong to fold with only 12 bbs behind. as a short stack, i'm not afraid to get my money in with decent equity spots. i also block ak, aq combos as well as some qq, kk combos as well. so, we're likely flipping against middle pairs, have good equity against k/x, q/x hands, or slightly behind some a/x hands. not say being up against qq, kk, aq, ak isn't impossible, it's just a lot less likely. and if were up against aa, who cares? it's no different than having qq vs aa in this spot, so i don't even worry about that.
also, with 12 bbs i still have enough to squeeze and potentially get heads up, increasing the our preflop equity. i also have enough to potentially take the pot uncontested preflop, though it's highly unlikely as mp is getting ~2.3:1 to call in this spot. but, if it works, i increase i stack by 50%. so, getting it in this spot isn't a terrible overall. if i isolate and get called, i don't mind being in a ~35/65 spot or better with 10-12 bbs effective nor do i mind picking up an extra 50% of my stack uncontested either.
flatting is bad because I don't close the action and i'm put in a weird spot if bb 3bets or jams. i'm never just 3betting either because i don't have any fold equity and i'll have to reluctantly call if i get 4bet jammed. plus, if we 3bet and get called, we don't have any good cbets with our stack. if i had a hand like AKs or QQ, then i might opt to just 3bet with the intention of calling off a 4bet jam.