By NMR experiments. CH2 with primary amine has different chemical shifts than CH2 of secondary (and tertiary) amines. Using a long delay (10 seconds) you could compare the integrals you will obtained and know how many primary amines you have in your sample.
Another way could be to derivatize the BPEI with an aldehyde (benzaldehyde, for instance) and to check by NMR how many imine you have compared to the overall amount of CH2 in the molecule.