What is the meaning of the "the river is flowing?" Is this valid usage?
Websters, #2: River: A large quantity of a flowing substance
The river is already a flow by definition. Can the river be "not flowing?"
We would identify something as a river because we ordinarily expect it to have the characteristics of a river, even if some of those characteristics are temporarily suspended. That is, a permanent or semi-permanent stream would be a river even if it has temporarily stopped streaming, as noted in the comments, by drying up, being dammed up, or being frozen solid.
On the other hand, something which only temporarily takes on the characteristics of a river could be called so, metaphorically, but only while it possesses those characteristics. If they cease, the metaphor is no longer applicable. If I spill a jar of molasses, I may report a river of molasses running down the table leg, but once the flow stops, we would lose the river (having gained a pool).
Consider one's vocation. Someone who introduces herself as a pilot or a writer does not cease to be when she is not engaged in the act of piloting or writing. On the other hand, if I am speaking with my friend about two women across the room, one dancing and the other standing still, I might refer to the first as the dancer to distinguish between them. If she stops dancing, then she is no longer a dancer, and I will have to identify her otherwise-- unless she hands me her business card with "dancer" given as her occupation.
I think Webster's #2 here is letting us know that a river isn't only a flowing stream of water (like the Thames, the Rhine, or the Rio Grande), but a similar stream of any flowing substance - even substances that might be metaphorical. Hence, we can have a river of lava, a river of tears, a river of blood, a river of ants, or even a river of joy. Not all of these flow by default.
Take, for example, a river of people (such as at the start of a large marathon). It's not hard to imagine a commentator saying, "There was a delay for awhile, but now that the ambulance is out of the way, the river [of runners] is flowing again."
I don't find the river is flowing to be any more redundant than, say, the author is writing, the scholar is studying, or the breeze is blowing.