Where is an item that can allow Vivi to learn flare.

i think you learn it from black robe bought in dugerreo (not sure on spelling)

It's the black robe, but I don't know where you get it from

I'm not sure where about it can be actually bought (apart from possibly showing up at the Auction House in Treno), but I know the Synthesist in Daguerreo can synth a Black Robe from a Gaia Gear and an N-Kai Armlet for 8000 gil.

where can i get Gaia Gear from cuz i dont have any, and am having trouble finding some.

You may be able to buy it in the Black Mage Village but if not, you can obtain it at Oeilvert in a chest.