If you receive something in return you are supposed to deduct the value of what you received from your deduction. I'm sure that the tracking on this is non-existent, so it comes down to what you choose to do. But that's the way it's supposed to work. Of course, you get to value the miles in this case.
Cheers.
The receipt from ARC says, "For reference purposes, you did not receive anything of value from the Red Cross in return for this donation."
Apparently
either the miles did not come from ARC but rather are a "gift" from AA in appreciation of your charitable atttude,
or ARC believes they have no value.