Can’t access appl tv on my fire tvs

1. If you haven’t already, get the Apple TV app from the on-device Fire TV Apps & Games Store.
2. Launch the Apple TV app.
3. Don’t select the Free Trial option. Instead, there should (also) be a “Sign in” option. Sign in to the Apple TV app using your Apple Account credentials (not your Amazon account credentials). With iPhone, the QR code method should be hassle-free.
4. You may be asked once to connect to Apple for verification through a browser on computer or mobile.
5. Enjoy the Apple TV subscription service (and optional content purchases) on Fire TV, largely similar to what you get on iPhone.

References:

Get the Apple TV app on your smart TV or streaming device - Apple Support

Watch on these smart TVs and third party streaming devices - Apple Support

Apple TV app user guide for smart TVs and third party streaming devices - Apple Support

I saw an answer that said to make sure I was signed on via the settings (gear icon), but Apple TV doesn’t show up.

actually, it does show up on one of my fire TVs via the gear icon, but still displays msg Accept Free Trial

I think those other answers could refer to the gears icon for Settings inside the Apple TV app, not the gears icon in the Fire TV interface.

At this time, I would suggest to contact an expert from the Apple Support staff for further assistance. Contact Apple for support and service (phone numbers) or start your support request online (fill in “Tell us what’s happening”, then choose from chat/​email/​callback).