Think of the plumbing and your pump as two separate machines. The head loss in your plumbing is dependent on flow rate. However, the flow rate of the pump is dependent on head loss. So you have two curves. The head curve of the pump and the head curve of your plumbing. Where they cross is the operating point of the pump and plumbing. Change the pump and/or plumbing and the operating point changes.
But really you needn't place all that much importance on knowledge of the exact operating point. It really doesn't matter much. But if you must know, the best method of measurement, besides a flow meter, would be to use a pressure gauge and a vacuum gauge. To get total head loss of the entire plumbing, you must measure the pump pressure at the pressure side drain plug of the pump and the pump vacuum at the suction side drain plug. Once you have both measurements you calculate head as:
Return head = Return Pressure (PSI) * 2.31
Suction Head = Suction (in hg) * 1.13
Total Head = Return Head + Suction Head
Then from the pumps head curve, you can look up the GPM. However, this is only good for that pump.
If you want to know the flow rate for other pumps, then you need to determine your plumbing curve. The plumbing curve is the curve which defines how the plumbing head loss changes with flow rate. You can determine the plumbing head curve from your old pump. The curve will have the relationship of:
Head loss (ft) = C * GPM^2
where C is a constant for your plumbing. Since you have GPM and head loss from your old pump, C can be calculated. The equation can then be used to plot over any pump head curve to find the operating point.
However, I have a couple of spreadsheets that allow you to do this with little work. They are under "Pump Modeling Tools" in my sig. "GPM Estimate" will estimate the GPM for a number of pumps using one of several different methods. Once the plumbing curve is "Calibrated", you can then change the pump model in other columns to see what the new flow rate will be. If you have a vacuum gauge, use "Head2GPM" tab. If not, use the "PSI2GPM" tab.
Another spreadsheet is "Pump Cost" which will compare not only the flow rates between pumps but also the lifetime cost of pumps. This is useful if you are trying to decide if a pump is worth the cost and is normally used to determine if a variable or two speed pump is more economical over the life of the pump. For low energy rates, a two speed tends to win out.
But the real question is: What are you trying to accomplish?