You can use a simple permeability cell with the aroma compound of known concentration/pressure on one side, the film in between the cells and the analytical probe on the other side. By analytical probe, I am referring to an FTIR or a GC method. Such a cell would be easy to construct. Here are some references-

1) Aroma Compound and Water Vapor Permeability of Edible Films and Polymeric Packagings, J. Agric. Food Chem. 1994, 42, 2071-2075

2) Comparative Performance and Barrier Properties of Biodegradable Thermoplastics and Nanobiocomposites versus PET for Food Packaging Applications. Journal of Plastic Film & Sheeting, 2006, 22 (4), pp.265-274.

Either GC with TCD or ECD or HPLC analysis would be of tremendous help.

Thank you!