I've found a hair dryer generally doesn't put out hot enough air. A heat gun made for stripping paint or shrinking plastic tubing will do the job.

The principle is to soften the chip, which is mostly plastic (even clay chips) without making it too soft. The heat gun will reduce the chip to a puddle if not done carefully. I use a piece of ceramic tile and heat the chip in stages, dropping the chip on the tile as it gets gradually softer. When to the right temp, dropping the chip flat on the tile will result in a "clunk" rather than a "clink" and it's ready to be flattened. I've found that just applying pressure with my hand with the chip on a flat piece of (cool) tile will do the job. You may have to try several times to get it just right. This should not change the surface texture of the chip or increase the diameter if done carefully. I'd recommend experimenting with a cheap chip of the same type before flattening your "trophy chip" .