We should lean toward aggressive betting with top pair on the flop and turn, but shift to a defensive check-call on the river when the flush completes.
While checking is a viable mix to protect our range, betting is strongly preferred to extract value from weaker Ax, Jx, and flush draws.
Note: Checking misses a high-EV opportunity to build the pot with a dominant top pair on a board that offers plenty of second-best calling hands.
After checking the flop, betting the turn is mandatory to realize equity and regain the initiative on a board that is becoming increasingly coordinated.
Checking the river is a sound tactical adjustment once the spade flush completes, as our hand is now primarily a high-frequency bluff-catcher.