I don't generally clean chips, but when I do I go simple: a tiny bit of dishwashing soap or SoftSoap on my wet fingers, rub it, rinse it using my fingers (I don't soak a chip in water at any time, since clay is soluble). I dry it immediately, making sure to get the edge as well.

I do not use brushes or anything else that scratch the surface.

I do this mainly to remove the finger sludge that collects on some chips over time. I have not noticed any damage from my low-impact method. My biggest fear, though, is water seeping into a clay chip because I did not dry it well enough.