A learning remote can only be taught with IR remote, it can't learn bluetooth or any type of RF remote.

You can buy a device that allows fire stick to accept IR commands, xbox 360 IR commands. Its made by Inteset:

[Link: amazon.com]

Perhaps if you were to get UEI made remote with xbox 360 code, you could search advanced codes (EFC's) for these channel commands? Then teach them to your sofabaton?