Just make sure the vinyl film is still good and tightly bonded to the surface. If you're painting them a color, you can tint the Zinser 1-2-3 to minimize the number of coats you will need to cover. You can use either a latex or oil-based enamel...I assume that you aren't going back with white...but it you were, just know that oil-based enamels will yellow now fairly quickly. We have a client who insists on a high gloss while enamel for her cabinets....they yellow after a couple of years and she has HandyANDY out to repaint the again!
Then apply a high quality acrylic trim paint.
Best, Charles