Buy all the gear you need from the shops on the Invincible before you head to helm and begin flying. The shops are the little items. By pressing A in front of them you can access everything!
Additionally you have beds and a Fat Chocobo at your disposal. No more having to pay for inns!
The Invincible has a special ability to fly over small mountains. Go to Saronia Castle, then southwest to the mountains. Once you bump into them, go west into them. Once you leave the forest, stop and face south. Those particular mountains can be "jumped" over with the A Button .
Fly over them and continue along the path to soon reach Falgabard . Land and enter.