"The IRS currently recognizes the donation of frequent flyer points as a gift from the airline to the charitable organization, therefore miles donated to the Red Cross are not considered tax-deductible by the individual donor." (Red Cross)

"Income Tax Deduction on Awards:

The donation of miles is generally not tax-deductible. In essence, they are not "property" in the eyes of the IRS, and thus have no monetary value.

The reason for this is simple, you generally have earned miles as a non-taxable rebate from other purchases and have not paid exclusively for the miles in which to establish a donation." Mile Donor

Doesn't seem to be much doubt as to how the IRS construes it: You didn't pay for the miles, so you don't get a deduction.