Streaming · Plain-English answer
Yes. Amazon's Fire TV Stick runs Fire OS, a version of Android, so it supports VPN apps installed from the Amazon Appstore or sideloaded as an APK. Once connected, everything the Firestick streams goes through the VPN tunnel, which changes where your traffic appears to come from for every app.
Open the Appstore on the Firestick, search for your VPN provider and install its app the same way you would install a streaming app. Sign in, pick a server and connect. Fire OS treats it like any Android VPN, so the connection covers every app on the device at once.
If your provider has no Fire TV app, you can sideload its Android APK using the Downloader app after enabling apps from unknown sources in the Fire TV settings. Sideloaded VPN apps work, but navigating ones designed for touchscreens with a TV remote can be clumsy.
Streaming apps on the stick will see the VPN server's location rather than your own, which affects catalogues and availability exactly as it does in a browser. You still need valid subscriptions for whatever you watch, and some apps block known VPN ranges.
First generation sticks have slow processors that can bottleneck encrypted traffic, so if playback stutters, try a nearby server or a newer stick. WireGuard based apps put noticeably less strain on the hardware than older protocols.
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