Not possible.
The FM Radio requires an external antennae. The "wired headset" plugged into the audio jack acts as the antennae. You are allowed to play the radio either through the wired headset or the phone's speaker, but cannot stream it to Bluetooth for some reason. Personally, I have tried this. Using the wired headset plugged into the phone, leaving the phone on the counter and walking around the room with the Bluetooth headset while I get work done would be an ideal setup for me. I'd actually use the FM radio more often, but I can't chance getting the cord caught on things as I work.