Susan, I am no floor expert but we have had our oak hardwood floors refinished/repaired (and sanded, stained, and polyeurethaned) several times. There is no good way to remove these flathead nails without doing damage to your floor. What kind of subfloor is it nailed to, a plywood deck? is there crawl space underneath oris it on a concrete slab? How many flatheads did he put down and how many planks affected? If you damage one plank, will it be possible to replace a damaged one with a new one so that you can resand, stain, and varnish to make it blend in? If you have lots of nails in lots of planks you might consider tearing one plank out and using a flat prybar to pry all the others up (hopefully prying the whole planks up may prevent too much damage to the planks, then they will need to be renailed down with a finish nail and have the heads set down below the surface. However, if it was put down correctly to begin with it was probably nailed along the tongue as well (these should be tongue and groove planks) so that will complicate the removal too.
Give us some more info. as requested above, maybe someone else will have some bright ideas for you . Hope this helps. LJ