That won't work. Distilled white vinegar has to be replaced every 45-60 minutes because that's as long as it's effective, making it far too labor intensive to be worth the effort needed to use it to remove a serious buildup. A cupful or two every week, flushed all the way through the system, followed after 45-60 minutes with about a quart of clean FRESH water will prevent buildup, however. Never leave vinegar sitting in the bowl. When soft rubber (joker valve) is allowed to sit and soak in vinegar it swells and distorts.
Several "doses" of muriatic (hydrochloric) acid --available from any hardware store--used according to directions will do it, however.
--Peggie