After you attend the remembrance services in each city-state, you choose to join the Immortal Flames.
This quest is available if you have completed the quest A Hero in the Making.
Starting the Quest
Talk to the Flame Officer in the Waking Sands in Vesper Bay in Western Thanalan and say Yes, then accept the quest.
Speak with the Personnel Officer
Go to Ul'dah and use an aetheryte to go to the Aetheryte Plaza (if you are not there already). Go southeast through the hallway, then go southeast to the Hall of Flames and talk to the Flame Personnel Officer. There will be a cutscene. You can respond however you wish to the question.
Determine the Fate of the Airship and its Crew
Use an aetheryte to go to Western Thanalan via the Gate of the Sultana, then go northwest. The destination is just north of the bridge.
Speak to the Airship Crewman. There will be a glow around him, indicating an instanced battle. Check on him and there will be a cutscene, and then the battle will ensue.
Solo Duty: The Company You Keep (Immortal Flames)
Attack the Imperial Funditors and Imperial Imaginifiers first, then the two Bestiarius, and finally the Decurion. When the Magitek Vanguard appears, go off to the side, because it will sometimes target a random ally with Cermet Drill, a line attack, and if you stand off to the side, you can bait the attack away from your allies. Defeat the two Funditors that appear at the same time as the Vanguard, then finally attack the Magitek Vanguard until the battle ends.
Following the battle, there will be a cutscene.
Speak with the Personnel Officer Again
Go back to Ul'dah and use an aetheryte to go to the Aetheryte Plaza (if you are not there already). Go southeast to go outside, then go southeast to the Hall of Flames and talk to the Flame Personnel Officer to complete the quest.
Get a Chocobo
It is strongly recommended to talk to Swift to start the My Little Chocobo (Immortal Flames) quest. Upon completing this quest, you will receive your own chocobo mount. However, you should finish the next quest, For Coin and Country, before you proceed with My Little Chocobo, because the quest reward will help you complete it.
Next Main Scenario Quest
After you complete the quest, talk to the Flame Personnel Officer to accept the next quest: For Coin and Country. There will be a cutscene.