If your door has loose chips scrape off the loose paint,since this is metal if bare metal is showing you need to buy a metal primer. Then paint your door with 2 coats of acrylic paint.acrylic paint is more flexable and will last longer on items that have movement. These item can be purchased at
most lumber yards,lowes,menards,walmart
You should use a exterior paint and use a spray gun if you can get one