KK sb vs bb

I wonder if we could ever call here?
JJ, AA would 3bet pre, so value hands he can have are 55 (3combos) / 44 (1 combo) and 54 (6 combos)
bluff hands until turn are 7d6d, 8d6d, 8d7d, Ad2d, Ad3d but I don't see him shoving his Adxd on river, so that leaves only 3 possible bluffs in his range and we should instafold here??

PokerStars - $0.50 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: 106.54 BB (VPIP: 22.22, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 29)
Hero (SB): 100 BB
BB: 260.22 BB (VPIP: 25.00, PFR: 17.65, 3Bet Preflop: 3.03, Hands: 136)
UTG: 70.24 BB (VPIP: 18.27, PFR: 9.64, 3Bet Preflop: 1.24, Hands: 402)
MP: 132.24 BB (VPIP: 19.30, PFR: 11.75, 3Bet Preflop: 3.35, Hands: 509)
CO: 106.46 BB (VPIP: 40.00, PFR: 36.00, 3Bet Preflop: 27.27, Hands: 26)

Hero posts SB 0.5 BB, BB posts BB 1 BB

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

fold, fold, fold, fold, Hero raises to 3 BB, BB calls 2 BB

Flop: (6 BB, 2 players) J♣ 5♦ 4♦
Hero bets 3 BB, BB raises to 8 BB, Hero calls 5 BB

Turn: (22 BB, 2 players) 4♠
Hero checks, BB bets 17 BB, Hero calls 17 BB

River: (56 BB, 2 players) A♠
Hero checks, BB bets 232.22 BB and is all-in, fold