I'm sure they would if Netflix was paying - After all Netflix runs on AWS which they have no problem with! :)

I suppose the issue would be that Amazon are now directly competing with Netflix via their own video offering, so may be reluctant to give Netflix the means to outdo them at their own game.

In my own personal opinion, Amazon's UX for video is not all that great either, so it would seem both parties have plenty of room to innovate in this space at least, which can only be a good thing. I'm paying a subscription for both, and although I currently use Netflix more, it really wouldn't surprise me if Amazon started rapidly working on their video UX - they've got 'buying stuff' down to a tee, so it'll be interesting to see what they can do with streaming video.