Playing the skin flute is a slang phrase that refers to fellatio or masturbation depending on the context. In this particular phrase, the flute is another word for a penis.
Playing the Skin Flute
More About Playing the Skin Flute
The skin flute is a slang term for a penis. So, to play the skin flute by oneself is to masturbate. If another individual plays the skin flute on another person, it refers to fellatio or a hand job. The phrase can be used as a sly way to ask or tell another about masturbation or blow jobs in a public setting.