It is unusual to have a flare flow measurement application where parameters such as pressure, temperature, molecular weight, etc. are constant. If this is truly the case, it makes your task of selecting a suitable flow transmitters much simpler. One of the reasons flare flow measurement tends to be challenging is not knowing the exact composition of the flare gas, or the flowing conditions from hour to hour. This is why most flow measurement technologies (orifice plate, thermal mass, etc.) are unsuitable for flare service, because their calibration depends on gas composition and flowing density.

Mass flow measurement is usually required in applications such as custody transfer (buying and selling a fluid product) and for chemical reaction processes where it is important to maintain proper stoichiometric ratios of reactants. Volumetric flow measurement is more common than mass flow measurement simply because many mass flow sensor types are inherently volumetric: turbine, magnetic, ultrasonic, vortex, positive displacement, and such are all velocity-based. In most flow measurement applications, there is no disadvantage to measuring mass flow instead of volumetric flow, it's just usually more expensive to do so.

Coriolis-type mass flowmeters are incredibly expensive for their size, and therefore are used only when high-accuracy mass flow measurement is absolutely needed. Thermal mass flowmeters are a lot less expensive, but getting good accuracy on large pipes is a challenge because the thermal sensor only intercepts a small portion of the flowstream (like a Pitot tube) and so changes in flow profile can have a big effect. It is possible to force almost any volumetric flowmeter to act as a mass flowmeter by installing transmitters to measure pressure and temperature, then using a computer to calculate density and multiply the volumetric flow rate by that density to obtain the mass flow rate, but this requires a lot more instrumentation, setup, and calibration to do -- once again, more money.

If the density of your flare gas is truly constant, volumetric flow will always be directly proportional to mass flow, so it doesn't matter which type of measurement you choose. If I were you, I would make absolutely sure the pressure, temperature, gas composition, etc. are truly constant in your application before selecting any flowmeter. When I say "constant" I mean constant for ALL flare line conditions during which you expect accurate flow measurement.