How to paint Vinyl clad door frames & kitchen cabinets?

Use a blow dryer to soften the adhesive and peel the laminate off. Try to scrape off as much of the adhesive while its still soft. You may have to sand off the remaining adhesive. To paint the cabinets.

Make sure they are clean and dry. Use acrylic latex paint. Remove the doors and hardware. Mark the doors and cabinets with tape where they go. Lightly sand the doors and cabinets to remove any gloss and roughen the surface for paint. Prime with a stain blocking primer like Zinsser 123. Then paint with your color. Seal with at least three coats with a water based polyurethane. Use a small foam roller and foam brush for a smooth finish.

First problem you have is that unless you prepare it properly paint will not stick to the slick surface. And even with adhesion you will not have excellent results. There is always the chance of it peeling when nicked. An oil or shellac based primer must be used after the oils from years of fingers are cleaned off with a degreaser. Then look for a bonding primer. Paint this on and let dry thoroughly before recoating with the paint you want to use. Due to being handled opt for a semi gloss or high gloss paint. You might can try a whit shellac as a primer(BIN makes one and I am sure others do too. Parks used to make one also) The only problem with shellac is it may alligator on a slick finish and not be as good as an oil primer. You can not scuff up the cabinets with sandpaper because it might penetrate the film. You my be able to scuff it up with steel wool enough to deaden the gloss and give the primmer something to grab. The more able the primer is to stick to the cabinets the better the final finish will be.

That might be best....it is really hard to make that type of cabinet look good when they start aging. Good luck.