Hi, Linda. As you know, you are not painting on wood, you are painting on a picture of wood on plastic. I'm surprised that enamel didn't stick to it though since enamels will stick to styrene pretty well. But if it did not, then it is probably mylar and not much will stick to it. If you happen to have a selection of different types of spray paints, like lacquers and polyurethane, you might give them a try on small sections to see if anything works.
Since the enamel flakes off pretty easily, you will have to remove it before you try other paints. Henry in MI