I have ran into the same issue. It is knows that Netflix app in fire TV does not support Dolby Atmos nor Dolby Vision. Prime does only offer HDR ULTRA and few shows with ATMOS.
I did plug in a fire TV 3rd Generation directly into my receiver Onkyo nr656 HDMI port; and ATMOS sound did not work. My receiver keeps flashing ATMOS with no sound and not sure what is causing this. When switching to Dolby Digital Plus it works fine. Perhaps there is a small issue with the code or syncing between FireTV and receiver.
HDMI audio with support for Dolby Atmos
Tip: Dolby Atmos offers full support for Dolby Digital plus as well as other features, including the ability to virtually move sound focus through three-dimensional space.
I just now use my FireTV for other apps which are not available on my LG TV. So i'd rather stream Netflix and Prime from the TV directly and bypass in between hardware for better picture anyway. I streamed the latest show "Carnival Row" from TV Prime App with Atmos with no issues (I have an LG TV with eARC 2.1). My receiver kinda chokes little for few seconds before actually sound comes out (have to raise or lower volume or mute unmute to get sound). potentially it is my Receiver's fault or the HDMI cable with ARC Sync protocol. I even ran an 8K HDMI cable (High bandwidth) and did not fix the choking symptom. For now it works....
The following Amazon Fire TV devices currently support Netflix in Ultra HD:
Fire TV 2nd generation (2015) and higher
Fire TV Stick 4K
Fire TV Cube
Netflix is available in Dolby Vision and HDR on the Amazon Fire TV 4K stick. To stream in Dolby Vision or HDR, you will need:
A Smart TV that supports either Dolby Vision or HDR10 and Netflix, connected to your device via an HDMI port that supports HDCP 2.2 or later.
A steady internet connection speed of 25 megabits per second or higher.