Game-playing: To be totally overwhelmed by your enemy in an up-close-and-personal battle. To be flayed is beyond being owned or pwned - flayed is being completely abused and shredded by a better player. The term "flayed" is usually used when you have massive weapons and your opponent only has a knife or sword or fist and whups you badly.
Teammate: Look out - to your right!!!
You: Dang! *shoots rocket, throws grenade in direction of attack*
Flayer *running in, knife in hand*: OORAH!
Teammate: Dude, he flayed you bad.