Birds are used to being the only bird-sized things in the sky. They also have sharp beaks and no morals. No other flying thing stands a chance.
Unfortunately for those Amazon delivery drones that may or may not be in our future, territorial aggression + tiny flying robots = undelivered packages. As Slate points out, people with model planes and helicopters have been battling birds for airspace for years, and these package drones would probably face a similar struggle.
In the above video, a man's radio-controlled drone was attacked by a flock of birds. The birds hit it so hard it crashed to the ground. That's bad enough when it happens to your expensive model plane, but you'd be extra sad if a flock of birds pecked away at your mom's Christmas gift.
No matter what, Amazon's drones probably aren't hitting the skies anytime soon. Amazon still has the FAA and, ya know, technology to contend with.