How to use Fat Chocobo mount

[Niwashi]

It is a main story quest so you can't miss it.

No, it's not a main story quest. You have to reach a certain point in the main story before it's available, but the "My Little Chocobo" quest itself is a sidequest. (I'm guessing this is because it requires accumulating 2,000 Grand Company seals, which takes a while at that level, and they didn't want to halt the story there for that long.)

The main story will have you join one of the three Grand Companies, Twin Adder, Maelstrom, or the Immortal Flames. Once you've done so, then you can take the "My Little Chocobo" quest available at the GC headquarters. Completing that will give you a chocobo and unlock the ability to summon mounts.

[Bixillarla]

Yeah, I meant the joining of the Grand Company is the main story. Once you join there is quest right there next to you for the chocobo.

[Llamaskull]

Slight digression- I know you can join the three Grand Companies after Lv.20, but can you join the Garlean Empire?

[Failia]

Slight digression- I know you can join the three Grand Companies after Lv.20, but can you join the Garlean Empire?

That currently is not an option. It MAY be in future content (which I doubt to be honest given how they're made to be the bad guys for almost the entire main story quest and lore) but no, it's not available.

[Llamaskull]

Ah, well- so much for that. Would be pretty great, though.
I thought maybe it tied into PVP stuff or something. Want me some Magitek gear!