KK+flush draw. Some basic postflop questions

[barongreenback]

Party $200 6max. Villain seemed fairly tight preflop so far but I didn't have a lot on him. I intended to raise to $15 preflop but misclicked.

Party Poker No-Limit Hold'em, $2 Hero (6 max, 6 handed) converter

saw flop|<font color="#C00000">saw showdown</font>

CO ($160.93)
Button ($167.45)
<font color="#C00000">SB ($140.05)</font>
<font color="#C00000">Hero ($78.8)</font>
UTG ($94.25)
MP ($138.2)

Preflop: Hero is BB with K[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/spade.gif[/img]. SB posts a blind of $1.
UTG calls $2, MP calls $2, <font color="#666666">2 folds</font>, <font color="#CC3333">SB (poster) raises to $4</font>, <font color="#CC3333">Hero raises to $10</font>, UTG folds, MP folds, SB calls $6.

Flop: ($24) A[img]/images/graemlins/heart.gif[/img], 4[img]/images/graemlins/heart.gif[/img], 6[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, Hero checks.

Turn: ($24) 5[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">SB bets $15</font>, Hero calls $15.

River: ($54) 8[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks

How much to bet on river? I have $54 left (=pot).
I didn't bet the flop to avoid checkraise or stop and go but there are advantages to a bet. So, any different lines.

Thanks
James