What are the origins of alchemy in Fullmetal Alchemist? I noticed that in Fullmetal Alchemist: Brotherhood, alchemy didn't exist until The Dwarf in the Flask came into existence. I also noticed is that the great teachers of alchemy were Father in the West, and Hohenheim in the East.

So with this information, I think that if The Dwarf in the Flask was never created, then alchemy itself would never have existed. How were they able to obtain The Dwarf in the Flask?
It was never fully explained, when and how alchemy was "invented", but it's known that Xerxes was one of the first countries to know alchemy. It already existed when the dwarf in the flask was created, as he was created using alchemy. The creation of the dwarf in the flask just increased the knowledge because it knew much about alchemy and helped the alchemists gaining knowledge.