I painted my plastic shutters about 6 or 7 years ago. I think they still good. I mean its too cold to go look close, but I dont recall any flaking. I went from black to hunter green so it covered pretty good. The shutters were old and chalky, so after scrubing it left a bit of tooth for adhesion.
If you're concerned about adhesion, go to an auto parts store or auto paint store and get some plastic primer. Its used on car bumpers, plastic interior trim etc. You probably need the prep cleaner too, ask the paint guy. Good luck.