Just because people skydive with their pets, doesn't mean it's right. Plenty of people get there kittens and puppies high, which is really fucked up.

As for the military doing it. I'm not sure what purposes it serves, but sometimes animals testing as a mean justify an end, like testing cancer-curing drugs, etc. I doubt the military does it just for fun.

Why is this animals abuse:

• Animals cannot provide consent to something potentially dangerous (people have to sign releases before doing this, donkeys don't).
• In the highly unlikely situation that the donkey strapped itself up and that implied consent, it still does not understand the situation. Drastic change in environment (altitude, velocity, etc) causes shock and stress. Shock and stress can cause trauma, physical and mental, to humans and animals alike. These effects are worse if you don't understand that you're probably not going to die at the end.
• This act did not serve a purpose or an end that was a benefit to others (it was advertisement), so we can't ignore the above considers like we can with testing cures for diseases, military exercises, or space exploration.

NB: Remember that Rhino they airlifted a year or so ago? He was drugged up because they knew the experience could have caused unforeseen damage if he were aware of it. The reason he was airlifted was to save his life. That was justifiable; the use of this donkey for publicity is highly deplorable.