Cult Following: Eternal Flame
You can get this by talking to Lilith in the Resistance HQ in Sanctuary. Fast-travel back to Frostburn Canyon and head to the Incinerator Camp. Talk to Incinerator Clayton then use a fire weapon to burn bandits and collect their ashes. After collecting five ashes, return to Clayton to turn over the mission.
Cult Following: False Idols
Head to the marker and find Scorch. It's a large fire spiderant. Just keep distance and aim for its abdomen to deal critical damage. After killing it, return to Clayton to turn over this optional mission.
Cult Following: Lighting the Match
Open the nearby portalet then pick up the midget called Matchstick. Return to the entrance of the canyon then use the fast-travel station there to Southern Shelf. Head to the freighter and fight your way to Captain Flynt's stage. Follow the marker to find the incinerator behind the wall. Place Matchstick there then activate the lever to burn him. Return to Clayton afterward.
Cult Following: The Enkindling
Equip a fire weapon and light all marked effigies with fire by shooting at them. After lighting the effigies, head to the enkindling and pull the lever as instructed. Kill the cultists then turn in the mission to Lilith in Sanctuary complete it.