Some may have a single hex screw holding it's handle in place. If the faucet has two knobs each knob may be held in place with a Phillips head screw.
But a flat head screw? Maybe to pry a cover off something, but for that you could just use a butter knife. Flat head screws are more commonly used on electrical faceplates and barely anywhere else.
I have a flathead in my plumbing bag because sometimes those funny shaped nuts are so inconveniently located the only thing that will get to it is a really frigging long screwdriver.
Though if it's leaking...? From where? Won't shut all the way off or the drainage or around the faucet? I need more details.