How can I weather chalk-painted cupboard doors?

Yes you can rub stain easily there.

Thank you

Stain will stain the chalk paint. I would recommend dark wax if you are wanting to antique them. It's a little easier to use. You have a bit more control with wax. Stain can be very runny.

A dark wax would work beautifully. Keep in mind that you need to apply a clear wax first. Once you apply a clear wax you can use the dark wax over the clear but use it sparingly. Applying the clear wax first allows you to wipe off the dark wax if you get too much dark coloring than you would like. Use clear wax to remove some of the dark.

https://paintedfurnitureideas.com/trick-to-applying-dark-wax-to-chalk-paint

https://www.anniesloan.com/techniques/how-to-create-an-aged-look-using-dark-chalk-paint-wax

I agree. The wax is a better product to use.