Anime UK News reports that the following anime have been added to Amazon. They are not part of the new FunimationNow package which was recently added to Amazon. The titles below are available to Amazon Prime subscribers, but some of them can also be purchased (as individual episodes, or as a full season) by non-subscribers.
Flying Witch (pictured) here, 12 episodes, subtitled
GATE here, 24 episodes, subtitled
New Theatrical Movie Initial D Legend 1: Awakening here, subtitled
No Game, No Life Zero here, subtitled
Sonic X here, 13 episodes, dubbed, only available to Prime subscribers.
Yu-Gi-Oh! GX, Season 2 here (52 episodes) and Season 3 here (51 episodes), only available to Prime subscribers.
Of the current TV season, Amazon is streaming Boarding School Juliet here, IRODUKU: The World in Colors here and Karakuri Circus here. These titles are available to Prime subscribers only.