When you are choosing your move in a duel, hold your mouse over one of the moves so the description comes up. You will notice the moves are labeled physical or special. Special moves do damage based on your special attack stat. Physical moves do damage based on the attack (physical attack) stat.
The adamant nature increases attack but lowers special attack. Since flamethrower is a special attack, adamant is not the best nature to use this move. You can also see if a move is physical or special by looking at the bulbapedia website.
Flame wheel is the best physical fire move. Flamethrower does more most of the time even with adamant because of the higher base power, and most things you would use it on have lower spdef (Skarm, weezing, etc)