I just bought a Mi Box S b/c it was supposed to be able to play Prime Video.
I have downloaded and updated to the latest version (5.2.10-googleplay-armv7a) via Aptoide and the app appears to install fine.
I'm able to launch it and browse all videos. I am not, however, able to login. I've tried from the initial launch screen, from within the app's settings, and by clicking on a video to watch.
The only thing that happens is that I see the progress wheel spin for 3-5 seconds and then, nothing. No error, no message, nothing.
Got it working. Here's my solution for anyone else that might have this issue.
Because I'm in a non-supported country (I think), I had to install a VPN client on the Mi Box, switch to a US server, and then was finally giving the credentials/access code screen.