The typical order of painting is pros-aide (basically a primer used when painting latex), acrylic inks (craft paint or run of the mill acrylic paint won't work), then top coat with something like permawet. Your other option is rubber stamping inks or rubber cement thinned down with naptha and tinted with oil base paint, but that stuff is super toxic. You have to be sure you're using paint that stays flexible after it dries, and regular acrylic or spray paint doesn't. That's why it's chipping off. Unless you have a good primer/base coat, nothing you put on top is going to stick. Your best bet now is to strip off all the old paint and start over with the proper primer, paint, and clear coat.
Brian