I prefer to raise the flop. Against a set we'll stack off, against a lower flush we'll stack off, and against two pair we'll often stack off. Allowing a lower flush to see a free card kills our action when a club comes, and allowing a set or two pair to see a free card loses a lot of value. We're not getting an overcall here on the flop unless it's from the bare K (which is going to be rather rare here) so there's no real reason for a call imo.

As played, I think turn and river are correct assuming you called river raise.