"Activate dragon's fire and burn Matchstick" is an objective in the sidequest Cult Following: Lighting the Match in Borderlands 2
Walkthrough
Turn to the right of where you just hung Matchstick. You will see a lever. Give it a pull. This will send Matchstick into the inferno issuing from the Dragon's Mouth. Just head on back to Incinerator Clayton after that.
