For the FireStick, set the applications to auto-update in the FireStick settings: Settings → Applications → Appstore → Automatic Updates.
Alternately, you can force an update by going to the Amazon Appstore on the web and pushing the current version to your device (via the Deliver button).
Note that the FireTV version via the Amazon Web Store generally lags behind the version in the Google Play Store due to Amazon’s longer approval process. You can track current version of the AndroidTV app by following the Plex for Android release announcements. The version in the Amazon App Store is shown in the “Latest Updates” section (Go to app listing in store, scroll down to Latest Updates).
Do not sideload the Google Play Store version on your FireTV. It is not compatible due to Amazon’s Android customizations (it might load & run, but will be buggy).
