There is a way to calculate flow if you know pressure drop through a known obstruction. An orifice plate with a known Cv will allow you to calculate flow if you have a way to measure pressure up and downstream.
Air is a compressible fluid. Thus you need pressure (given) and temperature (missing) to determine its density.
Besides, CFM is a rate, meaning a time factor is included. If you have a bulk average linear velocity (also a rate) you'd be able to estimate the CFM.
Otherwise one should proceed by installing a Pitot tube, or any known obstruction measuring the friction drop, as ChrisConley suggests, which, in effect, is a step meant to estimate the bulk linear subsonic velocity of the fluid, or by the introduction of a tracer and its detection at two fixed points.