Checkboard has given a great description of the basic flow measurement systems. My only comment is that the second method (volumetric turbine meter), under the right lab conditions, is probably the most accurate. However those conditions are stringent:
1) Flow-straightening pipe (10x or 20x the pipe diameter) upstream of the meter, and a shorter one (5x perhaps) downstream
2) Lab-type hydrometer, temperature compensated
3) Software corrections for SG, fuel viscosity and BTU (LHV) content
4) Maybe some more I'm forgetting after a decade away from this game
Only a high-quality test cell is likely to implement all this.
Needless to say, this is hardly practical for line operations, so the mass flowmeter is universally used today.