The finish on your fridge is a baked enamel. It would eventually reject anything you put on the surface.
prep the surface with a light sanding with a fine sandpaper, 220 to 320 grit works best. Then a good smooth coat of automotive primer, specially in the areas where you will be "cleaning" the chalkboard paint often. I would also do several light coats of the chalkboard paint in this main area as well.