Formula for the conversion Air Pressure into Flow

It can't be done. One can have pressure at zero flow in, for example, a balloon.

However, for a given piping segment (counting the fittings and their equivalent lengths, and the pressure drop through that segment), you can use the Colebrook equation, or some alternatives, to compute the flow. (Or vice versa, given the flow, you can compute pressure drop.)

Some names to search: Reynolds, Darcy, Weisbach, Moody, Hazen, Williams, and others. This is actually a fairly complex problem that takes some pretty sophisticated pipe engineering to address. Anil Kumar, et al., have published some spreadsheet techniques on this.

It also depends on local codes and which calculations they will accept, along with who does the calculations. These codes differ widely in their rationality. C'est la vie.