Haven't had to do this yet, but I'd say a Dremel with the buffer wheel and an according polishing compound for the type of finish. Be sure to use the low speed. High speed will likely take the finish right off if you're not careful. I think Zippo does this for free if you send yours in for service.
If you want to be gentle to your Zippos, cleaning a used chimney with a Q-tip and Zippo lighter fluid will do the trick. On brass finishes, you might want to try NEVRDULL polish, though it may scratch the finish very slightly. There are plenty of web-sites with plenty of advice out there. I don't mean to be rude but, just do some research. Keyword...Best way to clean Zippos.
hello there is no best way to clean just leave it the way it is as time goes maybe it will gain value but I would use cotton in every way you try to clean the zippos