The one-flush special is an act of masturbation. In said act, one first produces excrement into any given toilet. After this being done, the given person proceeds to masturbate without flushing, becoming aroused by the stench of his own feces, leading to an incredible climax. After the ejaculant is cleaned, the mixture of excrement and semen is finally flushed.
Tom: "Hey man I heard you jacked off in the grocery store bathroom"
Friend: "Yeah bro, I pulled off the one-flush special!"