Technically the CCFF does not pay taxes so deductions are meaningless to a non taxable entity. This is the best money laundering scheme devised by anyone to date. Even the drug cartels haven’t come up with one as good, not even close.
No, they don’t take deductions, but they do have to account for the money. When they “donated’ the money to their own foundation and then paid Chelsea’s salary with it, they avoided the gift tax.