Erosnow, the Bollywood movie entertainment production group has signed a deal to offer its on demand service to Fire TV. Eros International is a publicly traded company on the NYSE and has been a big player in distribution and licensing of the latest Hindi, Tamil, and other Indian language movies and TV shows across Fire TV users. The huge library of films will be accessible to users across US, UK, and Western Europe.
To access the movies, navigate to the Amazon App store and install the ErosNow app. From there, you will be able to search and watch movies similar to Netflix.
I browsed a bit and you can watch popular movies such as Bajirao Masani, Piku, Kis Kisko Pyaar Karoon, Calendar Girls, Kuch Kuch Locha Hai. You can see the rest of the most popular Hindi movies here.