What does the symbol on Edward's coat mean? In FMA, the back of Edward's coat shows this symbol:



I can't figure out what it would be a reference to in-universe, because the symbology seems Judeo-Christian (a cross and what looks like it could be a serpent), and the show doesn't really have any Christian symbology in it. Is this some symbol in real life? What is it supposed to mean?
It's called the Flamel (yes, named after Nicolas Flamel, purported to be an alchemist who sought the Philosopher's Stone).

It is most noticeably similar to the symbol of Hermes, a god of alchemy, and also the Rod of Asclepius, which you may recognize from ambulances as the EMS symbol.

 

It is not a religious symbol, nor is it ever explained to have a relevance in the FMA universe. However, given its real life links to alchemy and medicine, it's safe to say that the author intended to bring forth real-world alchemical symbols into her universe.

Further reading: FMA Wiki entry on the Flamel