I can stream shows stored on my computer to my TV with Fire Stick but I use a MiFi device to handle that routing. Some form or router / Network setup is required but does not use any of your data limit to stream locally.
The Fire Stick is designed to be used with a live internet connection to take advantage of the many shows and programs available for free or paid in the Amazon library. I am luck to have unlimited 4G with AT&T for $20/month so I use the device almost daily along with my DirecTV service.