The Flamel refers to the mystical and alchemical symbol depicted as a cross with a snake or serpent draped about it, as well as detached wings and a crown above it.
It resembles and shares common origins with many ancient symbols (which it is often mistaken for), such as the Rod of Asclepius (the ancient Greek sign of medicine), the Caduceus (the ancient Greek symbol related to the god of Alchemy, Hermes) and the Serpent Cross (a Hebrew sign signifying victory over the devil). It is also one of the symbols attributed to the medieval professed French alchemist, Nicolas Flamel. The cross appears in Flamel's grave illustrations and many say to symbolize Flamel's relation to the Philosopher's Stone.
In Alchemy, the Flamel represents the "fixing of the volatile", a vital step in the alchemical opus' process, related to the making of the mercury's elixir and of curative processes.
In the Fullmetal Alchemist series, the Flamel symbol is the mark depicted (along with wings and a crown above it) on the back of Edward Elric's trademark red coat and on the left shoulder of Alphonse Elric's armor body. Though the manga does not explicitly state how the mark is significant to the Elric brothers, their alchemy teacher, Izumi Curtis also bears the mark, tattooed on her left collarbone, suggesting that the brothers share their master's alchemic symbol to show their tutelage under her.
In the 2003 anime series, Izumi states that the mark is that of her alchemy teacher, Dante. Above Dante's wooden chair in the library in her house, there is a golden statue of this symbol. Also, the Transmutation Circle used to weaken Homunculi is centered around this design.