Depending on WHY you want to know about flow, and what flows are involved, two "answers" may be available....
a) Keep an eye on the pressure in the pipe, or the pressureS at two well chosen points.
b) Why does the water move? If it moves because of a pump, just monitor the electricity going to the pump.
(I'm not calling anyone stupid with that second suggestion.... well, unless you include me in the group. For YEARS I looked for a way to watch for leaks from my domestic water system at times when I'm away from the house... before realizing that as I am on a well, monitoring the well's pump would alert me to a leak.)