I know how to change the refresh rate setting to 24Hz by holding rewind and up together for 10 seconds. The problem is that it doesn’t stick! Sooner or later it changes back to 60hz?
Changing back to 24 is a pain in the ass - waiting for all the display settings to cycle through until 1080/24 shows up 
How do you make the 24p setting stick permanently?
I don’t think the Firestick has auto refresh rate matching.
Some apps have it built like Kodi, Syncler and Stremio.
Some iptv apps have it also.
Not sure what app you are using to watch content.
I use Netflix, Stremio, and CinemaHD on the FireTv Max 4K. I hard set the unit to 24hz and output is fine for a while. But then a week later it defaults back to 60.
Trying to figure out how to make the 24 permanent.
I am not sure as I only use apps that have auto refresh rate feature.
Not sure if Netflix or CinemaHD has ARR.
I think Stremio has it in settings.
Not sure why your Firestick is switching back to match you TV refresh rate either.