I was hoping to smooth call the turn, and beat weak on the river hoping he would come over the top of me with a straight. How would you play this?

PokerStars No-Limit Hold'em, $0.10 BB (9 handed) converter

BB ($18.40)
UTG ($5.95)
UTG+1 ($23.30)
MP1 ($4.25)
MP2 ($19.40)
MP3 ($2.30)
CO ($10.05)
Button ($9.40)
Hero ($10.05)

Preflop: Hero is SB with K, A.
6 folds, Button calls $0.10, Hero raises to $0.3, 1 fold, Button calls $0.20.

Flop: ($0.70) 8, 6, 5 (2 players)
Hero checks, Button bets $0.4, Hero calls $0.40.

Turn: ($1.50) 7 (2 players)
Hero checks, Button bets $0.9, Hero calls $0.90.

River: ($3.30) 3 (2 players)
Hero bets $0.5, Button calls $0.50.

Final Pot: $4.30
Main Pot: $4.30, between Button and Hero. > Pot won by Hero ($4.30).

Results in white below:
Hero has Kd Ad (flush, ace high).
Button has 9c Td (straight, ten high).
Outcome: Hero wins $4.30.