If the flathead method fails to work, sometimes you can coax them into turning with some penetrating lube and a bit of time, then using the corner of a small cold chisel (or the like) engaged with whatever chunk metal is left on the cap to break it free to begin it turning in the right direction. Then needlenose pliers or, my favorite, a hemostat clamp, to grip it and turn it out all the way.
Needlenose vice grips can also help grab it...filing flats on the edges of the screw can help.
You could also try the tiny EZ-outs, depending on the size of the screw.
Or my favorite trick in desperate times, an appropriately-sized left-hand drill bit. As it drills in, it turns the screw counterclockwise and out.