If you know how many heads you have, and the GPM (gallons per minute) rating of each head, then you just do the math. This will give the worse case scenario, of course, assuming each head is adjusted for max.
If you can run each zone for 10 minutes, check the meter reading before and after, multiply by 6 to get the gallons per hour.
I just found this from Toro. Each manufacture should have similar details. The pdf shows how you can determine you're available flow rate (GPM) vs pressure (PSI). This also shows the usage of their heads at a given PSI.
Something cool I did last summer. My friend lives in a condo, he wanted to know how long and what time his sprinklers were running. We could not tap into the timer, or the valve, so this is what I came up with. I put a funny pipe "T" into a head in his back yard. This was up against the foundation, made it easy. At the 1/2" threaded port of the "T" I screwed an automotive oil sensor to it (using an adapter, standard NPT thread). This is the type used for gauges, not the switch type used for idiot lights. Previously I tested the sensor with my air compressor to see what the resistance was per PSI. Now all that was needed was to run a twisted pair of wires from the buried sensor into his basement. From there I designed and built a microprocessor circuit that would give him all the data he needed! We monitor date and time stamp, and continuos pressure. He can now tell what time of day he is watering, how long, and the pressure tells him if things are normal, or perhaps a broken head somewhere in the zone. You could use the same to monitor pressure, and convert that to GPM for a constant monitor of you're system. I went into this elaboration of detail, because I see you are a fellow EE guy from you're profile! Have fun with it!