I didn't have enough hands on this player to get a good read but I thought... It was a good line. How could I have better represented a flush here. During the hand I actually put my opponent on AdJ. As when I led into him on the turn I was trying to represent the flush. When he cold called I thought he might have the ace of that suit and be drawing.

Should my turn bet been a check raise or bigger? And should my river bet been bigger?

No-Limit Hold'em, $0.10 BB (9 handed) - Hold'em Manager Converter Tool from FlopTurnRiver.com

Button ($16.55)
SB ($8.20)
Hero (BB) ($10)
UTG ($10.80)
UTG+1 ($5.75)
MP1 ($10)
MP2 ($5.05)
MP3 ($3.40)
CO ($13.75)

Preflop: Hero is BB with J, K
2 folds, MP1 calls $0.10, 2 folds, CO calls $0.10, Button raises $0.20, SB calls $0.15, Hero calls $0.10, MP1 calls $0.10, CO calls $0.10

Flop: ($1) 7, J, 9 (5 players)
SB checks, Hero checks, MP1 checks, CO checks, Button bets $0.40, 1 fold, Hero calls $0.40, 2 folds

Turn: ($1.80) 8 (2 players)
Hero bets $1.10, Button calls $1.10

River: ($4) 5 (2 players)
Hero bets $2.20, Button calls $2.20

Total pot: $8.40

Results in white below:
Button had A, J (one pair, Jacks).
Hero had J, K (one pair, Jacks).
Outcome: Button won $8