Can I use chalk paint to paint over these kitchen cabinets?

That's the magic of chalk paint! Go ahead, it sticks to most surfaces!!!

You can paint anything with chalk paint. I find it adhears to laminate better if you scuff the surface up with sandpaper, just a light pass over every surface so it isn't so smooth. That being said, because the kitchen gets so much use... cleaning , grease and handling, it is important that you consider how you are going to seal it. Wax takes a lot of upkeep in the kitchen, you might consider poly acrylic (I find it much harder to work with, but it makes the surface so much more durable and no reapplying every few months).

www.hometalk.com/diy/kitchen-dining/kitchen-dining-furniture/paint-kitchen-cabinets-with-chalk-paint-4094563

I did the exact thing! I covered an ugly laminate cabinet with chalk paint. Here's how I did it: https://bachelorettepadflip.com/2016/08/14/painting-laminate/

I used chalk paint on my bathroom vanity which came out beautifully. But then it started to chip. What do I do? I don't want to constantly be touching up the paint.