I haven't been playing enough lately and not familiar enough with $15s lately to feel good enough to answer for certain.
However, the keys here are:
1) How many stronger Kx hands are limped preflop from the avg player?
A) Not many with a kicker of 6 or higher, this is positive for shoving.
2) How many 6x or 7x hands are limped preflop from the avg player?
A) Plenty of hands. This is positive for shoving.
3) How many of those 6x or 7x hands will bet and call a jam?
A) I don't know for sure about 7x, but 6x is not likely.
4) How often does the avg player bet a flop like this with any two cards/many of their misses?
A) ?
5) How many flushes are possible here versus weaker hands that will call you? How often will they fold?
A) Don't know how many weaker hands will call you or how often they will bet/fold, but #5 is really the key to this situation.

idk.... i personally wont jam in this spot.....
Ur jamming basically a TP no kicker on a monotone board... with K2, its the bottom of ur value jamming range, since its the worst KX hand possible, and where ur dominated by villains likely K5o,K7o limped hands.... in this spot, we're basically putting K2, and A7 into the same category, a value hand Vs villains likely 1 card FD or combodraw hand range......
the board texture is relatively wet, presenting both 89,45,58,FD etc... drawing combos..... i really dont see a pot size bet here as a bluff..... ur essentially either flipping 50% vs 50% equity wise against his combodraw, or ur behind his Flush range....
at $15, i'm pretty sure villain is board texture aware, and isnt going to to something crazy on this monotone board.... at best, i would check call flop to evaluate a street, since im not overly happy with my TP, and fold on any (club, or T,8,A) turn card....