Is there a brush on clear coat for repainted plastic chairs?

Rustoleum has a spray UV clear coat protector

What did you paint the chairs with? If you used a spray paint for plastic chairs you really don't need to put on a clear coat. The paint is enough and should last for a few years before they need to be repainted again. If you painted with any other kind of paint--it might not adhere well to the plastic and peel off. Adding a clear topcoat is not going to make the paint stay on any better.

Home Depot and Amazon sell Painter's Touch clear in quart cans.

I better Redo them with rustoleum. The spray paint that I had used had no clear coat. They are dull and when I rub my finger across them it looks like chalk on my hand.

No spray paint has clear coat in it. You used the wrong type of paint if it's coming off. Rustoleum 2X or Krylon Fusion bond with the plastic. No clear coat needed.