Hello, DannyNewYork.
Welcome to Apple Support Communities.
From what I've read, you want to know how to change to your Bluetooth headphones when taking a FaceTime audio call. I may be able to help. Switching audio sources shouldn't be any different than you regular phone call. While on a call, tap the speaker button to switch to the speakerphone, or tap the audio button to switch to a connected Bluetooth device: While on a call on iPhone
If your Bluetooth headphones are not an option, you may need a headset with a microphone. You may also try routing your audio as well. Check out this article for more information: Stream audio from iPhone to your hearing devices Go to, Route audio calls.
Let me know if this helps.
Cheers!