I'd also bet the turn vs unknown. Players on NL2 often call the turn with Kx or even Jx.
You have to call his check/raise though - you have too good odds to fold, even if he always has a flush there. You need to call $0.69 to win a pot of $3.30, which means you need to have 20,9% equity to call. You have a 22,27% equity against a flush.
Board: K
5
J
6
Equity Win Tie
MP2 22.27% 22.27% 0.00% { 5h5s }
MP3 77.73% 77.73% 0.00% { KdAd, QdAd, JdAd, TdAd, 9dAd, 8dAd, 7dAd, 6dAd, 5dAd, 4dAd, 3dAd, 2dAd, QdKd, JdKd, TdKd, 9dKd, 8dKd, 7dKd, 6dKd, 5dKd, 4dKd, 3dKd, 2dKd, JdQd, TdQd, 9dQd, 8dQd, 7dQd, 6dQd, 5dQd, 4dQd, 3dQd, 2dQd, TdJd, 9dJd, 8dJd, 7dJd, 6dJd, 5dJd, 4dJd, 3dJd, 2dJd, 9dTd, 8dTd, 7dTd, 6dTd, 5dTd, 4dTd, 3dTd, 2dTd, 8d9d, 7d9d, 6d9d, 5d9d, 4d9d, 3d9d, 2d9d, 7d8d, 6d8d, 5d8d, 4d8d, 3d8d, 2d8d, 6d7d, 5d7d, 4d7d, 3d7d, 2d7d, 5d6d, 4d6d, 3d6d, 2d6d, 4d5d, 3d5d, 2d5d, 3d4d, 2d4d, 2d3d }