Just take a bucket of known size (e.g. 2 or 5 litre), open up the tap as you would for archival washing, and collect the water coming out of it in the bucket... Use a stopwatch to time how fast it fills up and you will know the flow rate in litres / second. Multiply that with your normal washing times, and you are done...
Or do you really need millilitre precision?
If I install an accurate tap control which I can mark off at a known flow rate via the water in bucket method then yes, that is certainly an option.