How do I paint my thermofoil kitchen cabinets?

I would try painting them with chalk or milk paint. Those paints are designed for repainting cabinets and furniture. You only need to lightly sand, then clean the cabinets before painting. You only need to minimally scuff up tne surface to make the paint adhere. My cabinets are wood, but I used milk paint on them: http://momhomeguide.com/my-painted-kitchen-cabinets-a-year-later/

I took all my thermafoil off, sanded the cabinets very well......most importantly part of this project as your paint will Perlman off from the glue left on the mdf board. I purchased the cabinet paint at Home Depot. Painted and lightly sanded 3 coats. Been. 12 years

and only had to do over the handle parts of the sink cabinets and the first to cutlery drawers.

If in good shape, just paint over it. Clean very well, remove all doors, drawers and hardware. Prime with oil based primer and paint with oil based paint. Will outlast and not wear off as fast as latex or chalk paint and doesn't need to be sealed.

You need to slightly sand it before applying the paint but not too much

You can just paint but really need to take steps for the paint to adhere well. This stuff is incredible for that. https://dixiebellepaint.com/slick-stick-new-sizes/?aff=212 ..if you decode too remove, simply use a heat gun to make the thermofoil release

I would strip it all.