20 NL 6-max river decision

Do you push the remaining $6 and change or check behind on river? Do you think that the kings are good here?

Prima Network No-Limit Hold'em, $0.20 BB (6 handed) Hand History converter Courtesy of PokerZion.com

MP ($72.03)
Hero ($21.35)
Button ($39.69)
SB ($36.21)
BB ($19.20)
UTG ($19.90)

Preflop: Hero is CO with K[:diamond:], K[:club:].
1 fold, MP calls $0.20, Hero raises to $1, 3 folds, MP calls $0.80.

Flop: ($2.30) T[:spade:], 5[:club:], 6[:spade:] (2 players)
MP checks, Hero bets $1.5, MP calls $1.50.

Turn: ($5.30) 7[:club:] (2 players)
MP bets $5.3, Hero raises to $12, MP calls $6.70.

River: ($29.30) 6[:club:] (2 players)
MP checks, Hero ???

Final Pot: $43

bet the rest. if he got the flush or the 6, well good for him. I think it is a missed spade flush rather than any of the above two though, maybe with a 7. He could also just have any 10.