If you can put a temperature sensor downstream of the heater, you can get a temperature rise, which will help figure out the flow rate.
What is this thing (Red arrow)?
84% efficiency rating.
200,00 btu per hour at 84% efficiency is 168,000 btu/hr.
Temp rise = 168,000/(GPM X 60 X 8.34)
Temp rise = 336/GPM.
Y = temp rise.
X = Flow in GPM.
Y = 336/X
X = 336/Y
If flow = 20 GPM, then the temp rise should be about 16.8 degrees from heater inlet to heater outlet.
If the water temperature going into the heater is 80 degrees, the outlet should be about 96.8 degrees at 20 gpm.
So, you can estimate the flow based on the temperature rise.
For example, if you measure the temp rise at 9.6 degrees, then the flow is about 35 GPM.
You should target a temp rise of about 11.2 degrees (30 GPM) to 8.4 degrees (40 GPM).
As you can see from the below graph, the temp rise at flows beyond 40 GPM does not go down that much.
Once you go below 20 GPM, the temp rise goes up very fast.
Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.
www.wolframalpha.com