Again, you can only get this during Extra New Game. To be eligible for this one, you need to have previously beaten the game by killing more enemies with guns than melee weapons. This one is also in the Mall in the bakery on the counter. Simply pick it up.
Alternate way: After beating the game twice, the flamethrower will become available even if you didn't kill more enemies with guns than melee.
Fun fact: During a normal playthrough, the poster on the counter will say "Freshly baked bread" and in extra new game, it says "Freshly baked Dead" with the BR crossed out with the newly added D.