Steve,
I don't speak for the water, but if my two cents is worth anything, I would venture to say that a flush valve at the furthest or lowest point should be all that is needed, not in every ring. Thinking about manual vs auto flush also might make a difference, but typically, if a valve is going to be opened for flushing purposes, then the higher volume of flow should allow more water through each path of the rings, pushing debris through each ring segment until it is pushed out the path of least resistance. I would love to hear other inputs as well.