How do I restore rusted nickle plating on a antique barber chair?

You're really not going to be able to make it look worth a hoot without either paint or re-plating. If you paint you'll need to steel wool or sand the rust away first or treat it some Ospho to kill any rust you can't get off. O'Reillys auto parts carries Ospho. Any good plating shop can re-plate it and they generally aren't that expensive. You can find plating shops in the yellow pages.