I've cleaned 2 or 3, with usable, but not perfect results. With the mirror out of the camera I immerse it in vinegar for a minute or so, then wipe the surface with a VERY soft tissue (toilet paper), rolled up, and applying no pressure whatsoever beyond the weight of the tissue itself. Then repeat the process using demineralised water, removing as much of the liquid as possible, but again with zero pressure.
The vinegar seems to produce a very, very slight reddish discolouration, but I am fairly sure hydrogen peroxide would be more corrosive. The fungus will have etched the surface wherever it has touched, so the mirror performance won't be any better - you will only have stopped it getting worse. If the fungus is bad, you are really much better off replacing the mirror. I use the mirrors from cheap Polaroids on the 35mm SLRs I've dealt with, but it might not be big enough for a Rolleiflex. I have a note of the dimensions at home, but not with me at present.
You will also want to treat the mirror platform to make sure there isn't fungus lurking there to reappear in the future!