They must go to the shop to run though a large grinder. The big railroads have a machine that make a smooth profile on the wheels. When I rode the Santa Fe Southern about ten years ago I watch a worker use a hand grinder to the do the same process. You can tell a flat wheel due to making a clanking sound traveling down the track. There is a good article on Wikipedia on the subject. I would post a link, but I can not get the copy and paste to work the forum.
The area of a flat spot is generally much wider than the relatively skinny portion of the wheel that is in direct contact with the rail. Even if the wheel was receiving enough force/friction to be self-rounded lack of a controlled impact would simply squish/grind the wheel into some other uneven dimension. The part of the wheel/rail that does suffer from routine friction/grinding is along the inner lip, but grinding that away won't get rid of a flat spot. Or at least that's how I understand it.
If the flat spot is small enough it could get repaired by the mere action of the rolling of the wheel. I have noticed that happen at least once on a Viewliner that I was in, on one of the Silver Service trains. There was a slight flat spot when I went to sleep. When I woke up next morning, it was pretty much gone.