BABA is indeed a 501(c)(3), but because of the amount of adminstration involved, we do not have 501(c)(3) member teams. At one time, BABA offered a program through the National Heritage Foundation whereby teams could pay $200 to join and have Public Charity status under the NHF umbrella. Due to a change in the tax code last year, NHF discontinued that program.
We do have some limited information (with links) on forming a nonprofit on the
Start a New Team page on the main website.
Good luck!