So you have a new Amazon Fire TV Stick and some Bluetooth Peripherals like the Sony Ericsson MW600 BT Headset or say the JBL Flip 2 Speakers, then you may want to smartly want to integrate them into your Fire TV ecosystem by paring them.
One of the best feature with the Fire TV Stick as compared to few of its competitors is the availability of Bluetooth. You can pair a new Bluetooth device by going to Settings -> Controller and Bluetooth devices -> Other Bluetooth devices -> Add Bluetooth Device.
I have paired 2 of my most used Bluetooth Peripherals and achieved the following -
1. JBL Flip 3 Bluetooth Speakers - Once paired you can play music through any of the popular Fire TV Audio / Video apps and listen to the Music even by turning off your TV. It is also useful if you have a large room and watching a video where you need to carefully listen to some dialogue. Pairing with the BT speaker enables you to bring the Audio closer to you.