Isn't current flow a wrong term?
"Flowing" qualifies state of flow

"Current is flowing" implies current not equal to 0.

It's semantically correct. Same as, "The river is flowing." 


  Websters, #2: River: A large quantity of a flowing substance


It describes the degree to which the flow is occurring (e.g. not zero).

The presumption of the question is wrong

"Current is flowing" does not equal "flow of flow of charge"... 

...it equals "flow of charge is flowing." 

At worse, it's redundant (not wrong). Typically it's just used as I described above (to indicate a non-zero quantity).

For non-English majors (like me!), here is more detail on this specific use case from english.SE.

Essential vs. temporary attribution

Here's a highlight from the English community (user Choster, a professional writer in Washington, DC):


  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  metaphor is no longer applicable.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).


Current is a flow and flows may be interrupted, suspended, and resumed. A charge does not lose its ordinary expectation to flow just because it is momentarily not moving. 

Flow is a rate

Electric current is the rate of movement, not strictly "electric charge in motion". Because this difference is subtle and has little impact on day-to-day design and analysis work, it's largely ignored (as it should be). 

A quantity "charge in motion" would have units of yes/no -- is it "charge in motion" or not? To be more useful we need quantities that describe the motion. 

That is why current is defined as the rate at which charge transits a normal surface. That is, current is the flow of charges, described by how much charge moves in unit time.

Perhaps it is more illustrative to see that "velocity" is not "meters in motion," even though velocity is describing the motion in units of meters (per unit time). 

Another way to intuitively grasp this idea is to work backwards. In ordinary practice we readily except the idea of "zero as a number" and in engineering (especially appertaining current) doubly so -- "The current into the lightbulb is 0-Amps."

The reason current can be 0, as a quantity, is because it is describing a rate.