This is an adapter that will send receive BT audio sent by your phone/tablet/computer/etc to anything you connect to its 3.5mm jack: headphones, the aux input jack in your car or home stereo receiver. These should work with Fire TV as BT headphones. Sound quality is decent (BT 3.0). Has a built-in mic for return audio, but the one I opened and tried was so bad that it is unusable.
The price for these is all over between stores in my area - from 50 cents to $1, $4, $6.75+, so this is a very YMMV deal but seems to be widely discounted and on it's way to clearance in most stores. I paid $1 for several yesterday, they're down to 50 cents today.
Various colors available and two different case designs, but all appear to share same SKU and UPC. Happy hunting.
YouTube video reviews (not mine):