Flat-footed: "A character who has not yet acted during a combat is flat-footed, not yet reacting normally to the situation..."
Delay: " By choosing to delay, you take no action and then act normally on whatever initiative count you decide to act...
The RAW would seem to say your fighter would remain flat-footed. However, Delay is under Special Initiative Actions. Although you are taking no action, it is of itself, a type of action. Therefore, I would say you've met the "acted" requirement and no longer be flat-footed.