Does Flash Of Cameras Damage Coins?

No, not at all. You're probably not going to like the results a flash provides, but it isn't harmful.

Any light strong-enough to damage a coin will have other problems you won't enjoy, like burning your finger off if it gets in the way.

Ah good that is what I thought. Guess I was thinking of old paintings.

EDIT: Fixed typo.

I think what you are thinking about is the long term affect of light on art work. A museum has to effectively light art work and sculpture so that it can be examined and appreciated by the public but also not damage the work with UV rays.

As far as metals go, it is the heat, not the light that does the damage Tungsten filament bulbs in halogen lamps, create a substantial amount of heat. While sustained exposure could cause damage the heat generated in a flash will not.

Tarnish and fingerprints might darken more rapidly if given prolonged exposure to light, especially on silver coins; that's about the only effect I can think of that light could have on coins. The brief flash from a camera won't hurt them.