Eduardo Flamingo was an ordinary man with his own family who used to struggle with some criminal organization named the Mob. It lasted until they caught him and brainwashed into serial maniacal killer who eats faces of his victims. He killed all members of his family and then became contract killer whose "kill record is impeccable".
Major Story Arcs
Batman & Robin (Pre-New 52)
Eduardo went to Gotham City to deal with such major threats to the criminal underworld as Batman and Robin. After arrival he chased Red Hood and Scarlet to their lair, he shot the Red Hood straight in the head, thus shattering his helmet.
As Red Hood lay shaken from the shooting, Flamingo intended to finish him off. However Scarlet quickly intervened. Flamingo choked Scarlet with his whip and attempted to pull off the mask that had been melted upon her face. Red Hood screamed in protest, stating that it is the Red Hood who he truly wants to punish. The Flamingo released Scarlet and shot Red Hood twice; tearing off part of his ear and knee-capping him. Batman and Robin soon arrived to stop Flamingo from killing Red Hood. The Dynamic Duo were able to keep Flamingo occupied until Batman was thrown off an edge and Robin was shot five times at point blank range in the back.
During the fight with Batman and Robin, Scarlet was able to get behind Flamingo and proceeded to "let the punishment fit the crime" by slashing the right side of the assassin's face. The Flamingo was then hit by Jason driving a bulldozer, while trying to recover from Scarlet's attack. Red Hood then dumped a mass of rubble onto Flamingo. It appeared as if he was killed, but there is no sign of a body when the authorities arrived. Moreover, he was seen in the post apocalyptic future where Damian Wayne became the Batman (Batman #666).
A Court of Owls
For more information see : A Court of Owls
While Batman investigates Dan Matthews, a guard at Arkham Asylum who maybe on the take, Dan in a desperate attempt to get away, opens several of the inmates cells. Flamingo is one of those inmates seen attacking the Batman before the Joker (Nightwing in disguise) appears to come to Batman's aide and the pair work together to beat back the group of rampaging inmates.
Brave and the Bold
During the episode "Knights of Tomorrow!" Robin is shown punching both Pyg and Flamingo. Both of these villains were introduced/prominant in the Grant Morrison Batman and Robin comics.
When Jim Gordon is targeted by multiple assassins he and Officer Parks and the Captain Nathaniel Barnes kill or disable all of them. Eduardo Flamingo is called in to finish the job. He is a cannibalistic maniac who kills 4 officers in seconds and then threatens to eat them and then have Jim for "dessert". Jim defeats him in hand to hand combat and decides to let him live rather than killing him. Flamingo then kills Officer Parks while he is being brought to jail, causing Jim to question his decisions yet again.