It appears they've left it as the responsibility of app owners to add AFR if you have Android TV/Shield of which there is Kodi and the IPTV app Perfect Player that have the functionality (along with the French service Molotov), yet the big apps like Prime Video and Netflix don't.
I guess if it requires an app to implement it then it isn't quite 'automatic' - just as the Amazon Fire TV isn't? (AIUI it's quite difficult to implement AFR on DRM-ed content?)
The new 4K Fire Stick has AFR on some apps including Prime Video and Plex, but not Netflix which as you say isn't automatic. I'd expect AFR to be on the new Fire TV Cube when it's finally released in the UK.
Amazon (and I believe Apple and Android TV) haven't implemented Automatic Frame Rate switching in their core video playback functionality - i.e. when you send it 23.976, 25, 50, 59.95Hz content it doesn't automatically, at an OS level, automatically switch frame rates.
Instead they've introduced app-controlled frame rate switching using an API supported in certain OS releases on certain hardware. AIUI the API the app can, optionally, tell the OS to change the video output refresh rate (if supported and enabled). This requires the app to be coded to support that API and report the correct frame rate to the OS. It appears to the end user as if it is automatic, not manual, but at the app level, it isn't automatic, and has to be coded for. AIUI the reason for this is that it's difficult (impossible?) to probe DRMed content to discover its frame rate prior to decryption, and for security reasons, de-DRMed content that could be probed isn't easy to access (for obvious security reasons)
Some Amazon apps support this app-controlled frame rate switching, most (all?) Apple TV apps seem to, and very few Android TV apps appear to... (Whilst Amazon's Fire TV OS is a fork of Android, it differs from Android TV in how it signals frame rate to the underlying OS) I believe in Fire TV OS it's known as 'Cinema mode' as it's main reason to exist is to output 23.976Hz content at 23.976Hz, not with 3:2 at 59.94Hz (as previously the case). Given that almost all US high-end OTT content on Prime Video is 23.976Hz - this makes a lot of sense...
I'd expect all new Amazon hardware to support the Cinema Mode API and all future Fire TV OS releases to support it on newer hardware.
(Newer Roku solutions do this for pretty much every source I can find - but I don't know if this is handled at App level via an API or whether the OS handles it automatically.)
UKnews and London Lite gave kudos