River Value Bet?

[GTSamIAm]

Should I gone for the river value bet? I bet the turn to prevent free cards for flush draws. My logic at the time of river checking is thinking no hand is going to call me that I beat with the flush draw. My range of calling hands was K good kicker to A moderate kicker. A bad range to value bet into. Is this thinking correct?

Party Poker 0.5/1 Hold'em (9 handed) converter

Preflop: Hero is SB with K[img]/images/graemlins/club.gif[/img], J[img]/images/graemlins/heart.gif[/img].
<font color="#666666">1 fold</font>, UTG+1 calls, <font color="#666666">3 folds</font>, CO calls, <font color="#666666">1 fold</font>, Hero completes, BB checks.

Flop: (4 SB) A[img]/images/graemlins/diamond.gif[/img], 7[img]/images/graemlins/spade.gif[/img], K[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(4 players)</font>
Hero checks, BB checks, UTG+1 checks, CO checks.

Turn: (2 BB) 6[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(4 players)</font>
<font color="#CC3333">Hero bets</font>, BB folds, UTG+1 calls, CO calls.

River: (5 BB) 8[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
Hero checks, UTG+1 checks, CO checks.

Final Pot: 5 BB