The flute that the Moogle gives you, the one that lets you save on the world map. You can not use this particular flute "inside" because you should be able to find a Moogle to save your game.
That is, indeed, the correct answer. Depending on where you are standing, our Moogle friend can sometimes slide towards you over mountaintops and across the ocean. I thought using the word save in the riddle might give you a little clue. You're up!