BTN is a very loose regular, who cold calls BTN 19% of the time.
This is what his range may look like:


On the river, BTN will have missed open enders, few missed diamond draws and few missed pair + FD hands. He can have the club flushes as well, but 8 & 9 block a lot of them.
SB is a "fast and loose" fish, who doesn't quite know what he is doing. I already caught him once donk bet bluffing river. I think fish in this spot are so often full of it. And for what ever reason, fish tend to bluff multiway pots when they really shouldn't. Based on timing tells as well, I'd expect him to be bluffing like 75% of the time. SB can have missed draws (maybe gut-shot as well). I also give him a random 54o bluff for trying to steal the pot with a bluff. For value he can have a weak flush that he is unsure about, but again 8 & 9 block those significantly.
I'm mostly worried about BTN though.

Putting it all in equilab, here's the results I get:

CO 55.83% 55.83% 0.00% KhKs
BU 33.49% 33.49% 0.00% QdQh, QdQs, QdQc, JTs, T7s, 76s, KcQc, AcJc, KcJc, QdJd, QcJc, AcTc, KcTc, QdTd, QcTc, Ad9d, Kd9d, Qd9d, Jd9d, Td9d, Tc9c, Ad8d, Kc8c, Jd8d, Td8d, Tc8c, Ac7c, 9d7d, 8d7d, Ac6c, 8d6d, Ac5c, 7c5c, 6d5d, 6c5c, Ad4d, Ac4c, 5c4c, Ac3c, Ac2c, JTo
SB 10.68% 10.68% 0.00% JTs, T7s, 76s, 54s, 7c5c, 7c4c, 6c4c, 5c3c, 4c3c, JTo, T7o, 76o, 54o


I get 24% pot odds, so I think I should call this off right?

10 NL (6 max) - Holdem - 4 players
Hand converted by PokerTracker 4

BTN: 144.08 BB (VPIP: 30.83, PFR: 21.72, 3Bet Preflop: 7.71, Hands: 2,196)
SB: 156.26 BB (VPIP: 43.14, PFR: 5.88, 3Bet Preflop: 0.00, Hands: 53)
BB: 99.5 BB
Hero (CO): 131.7 BB

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has K K

Hero raises to 3 BB, BTN calls 3 BB, SB calls 2.5 BB, fold

Flop: (10 BB, 3 players) 4 9 8
SB checks, Hero bets 7 BB, BTN calls 7 BB, SB calls 7 BB

Turn: (31 BB, 3 players) 3
SB checks, Hero bets 23 BB, BTN calls 23 BB, SB calls 23 BB

River: (100 BB, 3 players) 2
SB bets 44.94 BB, Hero ???? , BTN still in the pot....,

As played I fold. But I think more importantly you shouldn't be betting flop and turn. This flop hits their range more than yours and are you really trying to get 3 streets of value with this board? I'd personally rather check back the flop so you widen your non-cbetting flop range and call turn or raise/fold to 4 bet, to see a check-back river (depending on if BTN or SB bets)

checking back this flop is a serious underbetting.
I fold river, C-bet flop is mandatory, might bet a little smaller ott or even x\c, both seems fine to me.

Just fold with person to act behind. Not even close.