Hi @Switchit, welcome to the community.
There is anecdotal evidence of compatibility with the Firestick, yes. The Sony page doesn't specifically list it as a supported device, but as Bluetooth compatibility is often just a question of trial-an-error, it's likely to be much the same as pairing with any other device.
The reports we have seen refer to a need to power cycle both the headphones and the Firestick before pairing finally happens. Good luck!
Mick
