Hello Missariellenicolle,
Thank you for reaching out in Apple Support Communities. To help troubleshoot this behavior, we recommend to follow the suggestions outlined on Amazon's website for Fire TV with AirPlay. Here are the steps that's recommended by Amazon and may help:
Use Airplay on Your Fire TV Smart TV
To display mirror or cast content to your Fire TV Smart TV, link it to the AirPlay app on a supported mobile device.
AirPlay is only compatible with the following Fire TV Smart TVs:
- Toshiba 4K UHD (2020 Model)
- Toshiba M550 Series
- Insignia 4K UHD (2020 Model)
- Fire TV Omni Series
- Fire TV 4-Series
1. Go to Settings on your Fire TV Smart TV.
2. Select Display and Sounds.
3. Select Airplay & HomeKit.
4. Follow the on-screen instructions.
Here's the link from Amazon's website for you to reference: Use Airplay on your Fire TV Smart TV
Kind regards.