Here is a new source of an Amazon employee saying that the App is coming:
I would like to inform you Amazon video business team is currently working on providing service on NVIDIA SHIELD. We have been receiving numerous feedback up on this issue, and we have taken this issue as a top priority.
[...]
As our team is working constantly to provide Amazon video service on NVIDIA SHIELD, I humbly request you to show your kind patience.
Source:
Here is a Nvidia employee indirectly saying it's coming (translated from german):
To make it short, 2 people complain that Amazon Video is still not available on Shield even though it is working on Android TV already (Sony).
The employee answers that "they are continuously working on bringing the best and most famous Apps to Shield TV".
Then someone else says (paraphrased): "doesn't Amazon prevent a release?"
Employee then answers " A little more patience :)".
Source:
https://www.facebook.com/NVIDIASHIELDDeutschland/videos/286118175060421/?comment_id=286138091725096
Big news. This would truly become the ultimate streaming box regardless of ecosystem if Amazon Prime comes.