I would not try to refinish the flange, you can replace it fairly easily with a dumb bell. This is a tool for removing the flange. Once you get it out, you can take it to the hardware store and get a replacement. Make sure to reinstall the new one with silicone. I typically do not just replace the flange (as a plumber) I prefer to replace the whole waste and overflow at the time. This assures me the gasket below is still flexible and seals properly. In addition the cost of the whole unit is seldom more than $20.00. This will save you having to work on the unit in a few years when the bathroom is already finished.
Good Luck
Raymond
Master plumber

Removing an old drain flange can be difficult if it is corroded and aged. I had came across flange thats is so stubborn, it even broke my Dumbell tool. I end up cutting it with a Dremel tool to remove it. A few minute job end up taking hour. Not to mention the hassle of taking the old one to the plumbing store to match a new one. It can all end up be atime consuming task.
I do have a quick simple solution. It is call PresFlo tub drain replacement kit. It is a heavy solid brass in chrome finish, which can be epoxy over your existing old flange, it only take minutes to install and don't need any tools at all. Another plus side is, you never touch the body of the drain and therefore it will not have any leakage problem in the future.

You can visit http://www.surfacerx.com/refinishproducts.htm
click on the