@Thecowking
Amazon Video for Tablets runs fine on vanilla Android 4.4.4 -> FireHD tablet, rooted and running Cyanogenmod 11-20141008-SNAPSHOT-M11-tate (cheap capable tablet for Clash of Clans lol).
We use Prime quite a bit - aquarium supplies, automotive parts, and whatnot. Worth the membership just from shipping in our case, video is just a bonus.
What tablets won't run the app?