Contact your welding supply distributor. There is a hand held flowmeter available that you hold against the end of the welding gun. I think L-Tec makes it but I'm not sure. It uses a floating ball in a tube (similar to flow regulator gauges) to indicate gas flow rate. It is definitely not a precision instrument and is not adjustable, but it is handy for getting relative readings. You do need to release the drive roll to keep the wire from entering the opening. Mine was free from a salesman but I was told the price was around $5.
CHGuilford

Take off the nozzle and the insulator. Find a hose that will slip on without restricting the diffuser. Clamp or tape the nose to the gun so it can't leak. Cut the wire just behind the feed roll or set the wire speed to zero if that is possible. Pull the trigger for a second to move the wire ahead of the roll but don't pull it out of the tube.

Find a jug. One US gallon is 231 cu in or .1337 cu ft, allowing a coupe of cubic inches for headspace say .135 cu ft. If you don't know the volume of your jug but have a scale, then weigh the jug empty and full of water, subtract to get the weight of the water, divide by 62.4 to get cubic feet.

Fill your jug with water, invert it in a shallow pan of water pull the trigger to get rid of the initial surge of gas then put the hose under the neck of the jug. Time how long it takes for the jug to go from full to empty. Divide .135 (or whatever the volume of your jug is) by the number of seconds to empty it. The result is cu ft per second. Multiply by 60 to get cu ft per minute or multiply by 3600 to get cu ft per hour.

Don't let the hose be too far under the water or the back pressure might restrict the flow a little. An inch or so should be insignificant.

Lab accuracy zero cost.

Regards

Bill