The Fire Stone can be found on Route 114, Route 124, Fiery Path, by defeating the Charizard Balloon in Super Secret Training, and by receiving it from a Secret Pal.
Route 114 — There is a chance of recieving the Fire Stone as a reward for defeating Kindler Bernie in a rematch.
Route 124 — Give a Red Shard to the Treasure Hunter and he will give you a Fire Stone.
Fiery Path — The Fire Stone can be found in the area of the Fiery Path that requires Strength to access.
Super Secret Training — Get a top score in The Fire Stone Cup Begins! battle against a Charizard Balloon. Note that Super Secret Training is available only to "fully trained" Pokémon.
Secret Pal — A Secret Pal has a chance of fonding a Fire Stone if you give them the command "Pick up stones."