My TV has been getting progressively worse lip sync, this is now a few seconds off, just watching standard Prime videos on the TV’s build in Fire TV OS and internal speakers. I can’t find anywhere to adjust audio sync.
You could try clearing the Prime Video app. Go to Fire TV menu > Settings > Applications > Manage Installed Applications > Prime Video > Clear cache, clear data, force stop > then press the Home button on your remote. That action will clear out the app and cause it to start fresh.