Short Answer: If you want 7.1 audio, get a Nvidia Shield Pro. Especially if you want TrueHD + Atmos or DTS-HD MA / DTS:X.
FireSticks cannot passthrough either TrueHD or DTS (all formats) audio. TrueHD is transcoded by Plex Media Server. DTS is converted by the FireStick to Dolby Digital Plus.
In my testing, FireSticks do not output any 7.1 audio (at least when running the Plex app).
Note: The Amazon Cube v3 will passthru TrueHD + Atmos. However, for DTS, it passes only the lossy 5.1 core.
Longer Answer: Can’t help with FireStick 3rd Gen specifics, as I don’t have one. Here’s some tests I ran with FireStick 4K, 4K Max, & Nvidia Shield Pro.
FireStick 4K, 4K Max, and Nvidia Shield Pro are connected to HDMI inputs on a Denon AVR-X4300H.
The Nvidia Shield Pro direct played all audio formats. It delivered AAC 5.1/7.1 as PCM 5.1/7.1 to the Denon. All others were bitstreamed (passthru) to the Denon. Shield has Plex app v9.29.0.3347 & passthru = HDMI.
The FireSticks have Plex app 9.27.1.2953 (current in Amazon store). Plex app HDMI = Passthru. FireStick audio = Best Available.
Neither FireStick delivered 7.1 audio to the Denon. The Left Surround and Right Surround channels were either combined with the Left/Right Rear Surround channels or simply dropped.
Note: Direct Play / Direct Stream / Transcode describes what happens with Plex Media Server. The Plex client, such as the FireStick, can convert the stream to another format. If this happens, the Plex Media Server will have no knowledge of the conversion, and it will not be reflected in the Plex Dashboard or Plex Media Server logs.
AAC 5.1 Direct plays. Delivered as PCM 5.1 to Denon.
AAC 7.1 Direct plays. Delivered as EAC3 5.1 to Denon.
4K: Left Surround combined with Left Rear Surround.
Right Surround combined with Right Rear Surround
4K Max: Left Surround and Right Surround dropped. No audio.
EAC3 5.1 Direct plays. Delivered as EAC3 5.1 to Denon.
EAC3 7.1 Direct plays. Delivered as EAC3 5.1 to Denon.
LS combined with LRS. RS combined with RRS.
TrueHD 7.1 Transcoded to Opus 7.1. Delivered as EAC3 5.1 to Denon.
4K: LS combined with LRS. RS combined with RRS.
4K Max: LS & RS dropped.
DTS-HD MA 5.1 Direct plays. Delivered to Denon as EAC3 5.1
DTS-HD MA 7.1 Direct plays. Delivered to Denon as EAC3 5.1
Both: LS combined with LRS. RS combined with RRS.