It's a drum term to describe a grace note, or double hit, that's not quite together, but not quite separated enough to be perceived as a rhythmic subdivision. It's a way of "smearing" a hit.
I'm using it here to describe when two instruments are supposed to be playing the same note together, but aren't.
Flamming can also result when the drum (it's most obvious on drums) is picked at about the same level by two mics, where one is 5-10 feet further from the drum than the other. Normally the inverse square law works in your favor, but when the "far" mic is on a fairly quiet source like an acoustic guitar, you can get enough leakage in there to hear. It's something that should be fixed by re-arranging the mics or player's position before tracking.