this is really weird! Now, according to the plex web server config, remote access does NOT work. however, using plex web, macbook, ios devices etc. it DOES work (ports are all correctly configured etc.)
still plex web server config says it does NOT work
and when I try accessing the plex server remote using a fire tv it does NOT work.
I have a similar setup. Synology NAS, LG 4k smart tv, Fire Tv 4k. I dont use the fire tv to access the Plex Server I use the LG Tv plex app and dont have an issue. Are you using a VPN on the Fire Tv stick? The local ip on the Fire Tv should be able to connect to the local ip of the Plex Server the same way your other local ip devices are.