How can a squadron prove that CAP is a non-profit organization? 

The IRS has ruled that CAP and its subordinate units are exempt from federal income tax under Section 501(c)(3) of the Internal Revenue Code. This makes donations to CAP eligible for deductions from income by donors as “charitable contributions” to the extent allowed by law. 

Please see the following link for the IRS letter  

Please note that this doesn't mean that CAP units are exempt from paying state sales taxes. This is a different issue. Each state makes its own determination whether to afford CAP sales tax exempt status. Contact your wing legal officer to see if your state affords tax-exempt status for sales taxes.