David covered it well! I'd like to add that if you encounter any issues with the built-in options, check your Fire TV settings to ensure screen mirroring is enabled. Sometimes, a quick update of both your iPhone and Fire TV can resolve compatibility issues.
Also, keep in mind that the quality of your Wi-Fi connection plays a role in the streaming experience. A stable and robust connection ensures smoother casting. If you face any hiccups, troubleshooting the Wi-Fi might be worth a shot. Happy casting!