I have flattened prints by ironing for years. I iron my test prints directly on the back of the print. I see no sign of damage, but I would never do this with a fine print. For those, I use a piece of mat board between the iron and the print.

I also have prints that I dry mounted with an iron 30-years ago. No sign of any injury to the print, and they are still solidly stuck to the mount.
juan