Amazon added this about six months ago, but it requires another iOS device:
http://techcrunch.com/2013/09/17/amazons-instant-video-app-a...
http://techcrunch.com/2013/09/17/amazons-instant-video-app-a...
That's why you can use the Kindle app on your iOS, or Android, or web browser. Or Amazon Prime on PS3/4, Xbox One/360, Roku, iOS.
They don't have to kill the iPad; they just have to win every book reader.