I have relatives who use all sorts of paints mostly for ceramics, porcellin and fabric. The point of fabric paint is that you are supposed to wash it over and over again and it will still be on your clothes.
I would try calling the manufacturer of the paint.
Also, try toothbrush with toothpaste, toothbrush with spray-nine. These will not harm vinyl. Fabric paint may come off if you spend some time with a fingernail picking at it.