Hi Ian
Sounds like you need the equivalent of a leak down tester, used on engines to test for cylinder leakage.
Basically it is an orifice ( in the case of cars they use 40 thou) with a pressure gauge either side.
If you plumb the tester in at A in your diagram, and there is no air leak or flow both gauges will stabilize to the same value, the more flow the greater the difference in the gauge readings. So if you can either turn off all the valves and open one at a time to find the greatest pressure drop, or have them all open and shut off one at a time to find which one makes the biggest difference.
If you have no idea what size restrictor orifice to use between the two pressure gauges, you can put a shut off valve in, and use a bit of trial and error to get a meaningful reading.
Because it is only a comparison tool there is no need for absolute accuracy or calibrated gauges, you are just comparing the flow through the machine against the flow through the restrictor, and if it is significant it will show up as a pressure drop.
Hope this helps
Trevor