Can I connect my iPhone to my Insignia Fire TV

What iOS version is on your iPhone? If you've updated to version 15, try downloading a mirroring and streaming app like DoCast https://apps.apple.com/us/app/docast-cast-and-mirror-to-tv/id6446948344. It works great with Fire TV, mirroring with almost no delays. Just download it from the App Store and follow the connection instructions to your TV. It's important that the TV and phone are on the same Wi-Fi network. Alternatively, you can try apps like Replica or TV Mirror, but I've experienced some connection issues with them.

See the pic below (Airplay on Samsung 4 Series)

AirPlay 2–compatible TVs and other Products --> See all AirPlay 2–enabled smart TVs

If you find your device in the link provided above then --> Use AirPlay to stream video or mirror the screen of your ...

Else Plug a Lightning Digital AV Adapter or Lightning to VGA Adapter into the charging port on the bottom of iPhone. Connect an HDMI or VGA cable to the adapter. Connect the other end of the HDMI or VGA cable to the monitor, TV, or projector. If necessary, switch to the correct video source on the monitor, TV, or projector.

Connect iPhone to a display with a cable - Apple Support (IN)