What is the best way to paint vinyl clad kitchen cabinets?

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you can clean them with tsp which will dull the shine giving the paint a better surface to stick to. Most acrylic paints will do a good job of adhering to the vinyl and lastinG a long time. I painted over melamine cupboards in a bathroom 15 yrs ago and only recently got a small chip at the bottom of one door. I used Behr brand paint. They have a a paint and primer in one that holds up exceptionally well. You should use a satin or semi gloss paint, and a small foam roller will give you a smooth finish. Do at least 2 coats and wait 24 hrs in between. They will feel dry to touch but resist the urge to get it done quickly by putting on the second coat too early. After 24 hrs you can give a light sanding with fine sandpaper. Wipe off the cupboards with a damp cloth to remove any sanding dust before you put your second coat.