The AirBuddy works relatively well on the FireTV. Unfortunately in the free version, the term is limited to 30 minutes. Since the connection was not so perfect, I have not yet dared to buy me the full version.
For this definitely would have the free software to be optimized before I buy them.
Highly recommended if you'd like to show someone a short song or the like. Otherwise - test the Pro version and tell me how it is there with the connection so;)