One of an extremely homosexual nature to a point where that person is actually so outwardly homosexual, it is almost as if they are willing to rip off the pants of a person of the same sex. The term flute is used loosely due to the idea of the "skin flute" or penis. Therefore, a flute chaser is one who pursues the penis.
Anthony wasn't invited to the party because he's a flute chaser, I saw him stick a cucumber in his ass and say WHOOO!!