Forbes:  Trumping The Donald's $5M Offer For Obama Doc, by Robert W. Wood:

Tax lawyers, especially aging men losing their hair, should be forgiven
for looking past the numerous other aspects of this latest little Trump
tempest in a teapot to taxes. Surely Mr. Obama will ignore Mr. Trump’s offer, but if he didn’t, who is taxed? Could The Donald deduct the payment? Is there any taxable income to the President?

The tax law tries to get a piece of just about everything. Even so, I
don’t see any income to Mr. Obama. If he did produce the documents he
would not be selling them. He would merely be revealing them in exchange
for a donation. You don’t have income when you do a walk-a-thon for
charity, even if your miles end up causing someone else to pledge money.

But the charitable contribution that
Mr. Trump is surely assuming he would get on the off-chance that Mr.
Obama complies is another matter. Can Mr. Trump deduct the $5 million if
he gives it to Mr. Obama’s chosen charity? Whether or not it seems
fair, probably. …

As for Mr. Trump, even if (as seems likely) there’s ultimately no $5 million gift to charity, there’s another tax angle. I would bet that some expenses associated
with this gambit end up on his tax return as business expenses. After
all, there surely must be some respect in which even this latest from
The Donald helps to enhance Mr. Trump’s illustrious—and hard to
define—brand.