After you rescue Biggs and Wedge and the Tiny Bronco from Imperial scouts, you return to the Hall of Flames for your induction into the Grand Company.
This quest is available if you have completed the quest The Company You Keep (Immortal Flames).
Starting the Quest
Talk to the Flame Personnel Officer in the Hall of Flames near the Ul'dah Aetheryte Plaza to start the quest. There will be a cutscene. You can respond however you wish.
Speak with the Scion
Use a Vesper Bay Aetheryte Ticket (which you received after completing the quest The Scions of the Seventh Dawn) to return to Vesper Bay. Go into the Waking Sands and talk to the Scion of the Seventh dawn. There will be a cutscene.
Get Your Chocobo
If you haven't already, go to Ul'dah and use an aetheryte to go to Ul'dah Aetheryte Plaza (if you aren't there already), then go southeast through the hallway, then go southwest to the Hall of Flames and talk to Swift to start the quest My Little Chocobo (Immortal Flames). Now that you have completed "For Coin and Country", you have enough Flame Seals to complete the chocobo quest. (See the quest page for the walkthrough.)
Next Main Scenario Quest
After you complete the quest, talk to Minfilia to accept the next quest: Sylph-management. There will be a cutscene.