That would slow down everything on wireless, but might be effective if there's nothing else using it. If there are other devices, they'll be fighting for the bandwidth and may make things worse (remember wireless is half duplex).
The only thing I can readily think of is if you have a spare router, disable all the routing and DHCP functions so it's just a switch and AP, set a different SSID and connect it to a rate limited port on the Billion. Make sure the Firestick is the only thing on that wireless LAN.
(As always in considering these scenarios I find myself wishing for Cisco features, and it reminds me that I really must sort out my own home router)