I'm not sure what you mean by "gas diffusion". From what you write it looks like you are looking for some material that comes with a high permeability to oxygen? If yes, low-crystallinity polyolefines (such as polyethylene) will do a good job. Natural rubber does an even better one. I hope this helps.
I am doing some works related to the vapour transport behavior of organic hydrocarbons through EVA nanocomposite. please check the publication in my profile. I think it will help you.
I like to add some points to my answer. The diffusion of gas molecules through a polymer membrane is a transport process which depend on several factors. These factors include the nature of the diffusing gas molecule, nature of the polymer membrane like extent of cross links in the matrix, extent of free volume of the polymer etc.
High diffusion means that high free volume. If you want high diffusion selectivity, you should get molecular sieve in the pore design. However, for polymer-based gas separation membrane, the size-sieving polymer are very rare.