Watching twitch on the Fire TV (Stick) app is actually possible since the updates last year, but some features are still missing.

I logged into my account and was missing the tab for VODs of my followed channels.
So there is no easy way to find out what streams of your followed channels you may have missed. Even if you know you missed one, you have to go to their page first which especially is a nuisance if you follow alot of channels which you have to scroll through. Using the remote control to search for a channel is even worse, so not an option for me.
(Sidenote: there is no date on the VODs on their channel page)

I also find it kinda strange that there is a tab to "continue watching" (which doesn't include streams you only saw parts of live) easily showing you the VODs you had to search so hard for in the first place, if that makes any sense..

I hope we can get that tab for all the videos of channels we follow, just like the 'Videos' tab in the browser.
Thanks for reading,
Tris