Amazon's drone delivery system is great PR, but pretty far from reality for most places. To carry anything big, you need heaps of power, and heaps of power means hauling around some good sized batteries. Current flight times are about 9 to 15 minutes, depending on the setup of the multirotor.
Then there's the challenge of autonomous operation. GPS autonav is great when you've got wide open areas, but get into a city type setting where a couple meters one way or another means contact with trees/buildings/power lines and it's a recipe for disaster. Then there's the unexpected that you'd have to deal with -- bird strikes, dumb people throwing things/shooting at it.
I've got this one as a test bed for search and rescue/precision agriculture/forest fire location type applications, but I'll have to deal with many of the same problems. There are ways to deal with them, but they're mainly only good for a limited subset of situations that the copter might encounter. In short there's still lots of research to be done before Amazon's drone delivery system can take off.