First you need a Golden Chocobo. So basically, yes, you have the right idea in that you need to keep finding chocobo treasures to get to the air garden. You'll also need to have found the 6 chocograph fragments before you can get to the Air Garden. The six of them make a single chocograph for "Mist Ocean."
Once you find the Mist Ocean chocobo treasure, you'll get Choco's flying ability.
The Air Garden can be located at one of five places in the world. Look for a big black shadow on the ground. Then fly directly under it, feed Choco a dead pepper, and he'll put his left foot in, put his left foot out, put his left foot in, and shake it all about; he'll do a chocobo dance and turn himself about, and fly into the Air Garden.
The air garden can be:
1. Mist Cont. - A bit west of Alexandria
2. Right in the middle of the ocean
3. Outer Cont. A bit southwest of Kuja's Desert Palace, on the peninsula.
4. Forgotten Cont. - Northeast of Oeilvert.
5. Salvage Archapelago - East-Southeast of Chocobos' lagoon.