How do I cast Apple TV from my iPhone to my TV, I have a chrome cast device?

Are you talking about Apple TV the app or Apple TV the device? I am assuming that you are talking about the TV app on your iPhone.

There are two ways to cast your iPhone content to a Television. AirPlay and Chrome cast. Airplay can play content on devices that are enabled for AirPlay such as the Apple TV device and on Televisions that are capable of the Airplay feature. Chrome cast can do the same with chrome cast enabled devices. Note that both methods are separate and two different processes.

Some apps use the Airplay method and some apps use the chrome cast method. Some apps can use both methods.

Your Apple TV app on your iPhone can only use the Airplay method and you have a chrome cast device and therefore they are incompatible. Hope all of this makes sense.

Axel F.