24fps doesn't work on Amazon unless you wait for the screensaver to come on while in an episode.
Once you press a button to wake up the Roku, the episode upon hitting resume will be at 24fps.
Starting the app and an episode without waiting for the screensaver to kick in, it will only play at 60hz.
Under "Settings > System > Advanced system Settings > Advanced display settings" does your Roku have an "Auto-adjust display refresh rate" item? If you don't have this setting, don't bother to read the rest of this post.
If this is enabled, the Roku circuitry sends the signal output at the refresh rate used by the original source material, commonly 24 fps (frames per second), 25 fps, 30 fps, 50 fps, or 60 fps. Every time the source refresh rate changes, the TV must adjust its display to accommodate the new rate, which on many sets results in a short blackout or other display disruption that some find objectionable.
This can happen when starting/stopping new programs, when going in/out/between commercials, wherever the refresh rate of the source material changes.
If "Auto-adjust display refresh rate" is set OFF, the Roku converts and sends everything at 60 fps so the TV doesn't have to adjust on the fly and you don't get those frame rate transition disruptions.
The tradeoff here is that, non-60 fps sources may not appear as smooth without a Roku refresh rate adjustment, depending on whether your Roku or your TV does a better job of refresh rate conversion. You have to decide whether this change is worth it to you.
Please fix the Amazon app frame rate switching. Stupid bot reply.