Thin liquid films are a potential game changer in the quest for efficient gas separation strategies. Such fluid membranes, which are complementary to their solid counterparts involving porous materials, can achieve complex separation by combining permeability and adsorption mechanisms in their liquid core and at their surface. In addition, unlike porous solid membranes that must be regenerated between separation steps to recover a gas-free porosity, thus preventing continuous operation, liquid membranes can be regenerated using continuous liquid flow through the fluid film. Here, building on the self-sustained mobile film technique, we propose a simple experimental setup allowing direct quantitative assessment of the gas permeability of soap films stabilized by different surfactant types. Using a simple prototypical example involving O2/N2 mixtures, the measurement principle is first presented to establish a proof of concept. As the gas solubilities and diffusivities are known, the results of such experiments can be compared with microscopic models to disentangle the liquid core and surface permeabilities from a direct macroscopic transport response of the film subjected to a gas concentration difference. The same dynamical experiments performed for air enriched in CO2 indicate that the permeability of the soap film varies with the molar fraction in the gas compartment, a feature not observed for O2/N2. These experimental findings pave the way for the design of novel separation technologies in fields and situations where porous solid membranes are of limited efficiency.