Plastic chroming is done in an evacuated vessel and is vapour deposited onto the parts. You can't rechrome at home and the paint stuff is a poor alternative, this is a job for a man with the correct tools i.e. plastic rechromer.
They also do conventional copper/nickle/chrome plating on plastic using the 'baby shoe' method. First they paint on a coat of lacquer filled with condictve bronze powder. Once dry, the now conductive part will take on a heavy coat of electroplate copper which is polished then nickle and chrome plated. This is one process best left to the pros. No way to do it without 6-figure investment in specialty equipment, lethal chemicals like cycnide and EPA putting oyu in jail with the first bottel of chemical you open. If it could be done, Eastwood would have offered a home kit by now. Your peeling coating on your door handles is probably this type of coating since the vacuum plated coating may rub off but can't flake very easily.
Check in Hemmings. I am pretty sure you will find a shop that can do the job. Incidentally, if your car is a Chevy or Ford, most larger auto parts stores carry matching replacement knobs on those massive displays of bubble pack parts.
The parts in question are the in-dash light and wiper knobs. Mine were cobbled together at some point with a wood screw and some wire so I bought a pair on ebay for 9 bucks. Looks like if I have to pay for rechroming at some point I should have gone for reproductions. I'll have a look at hemmings.