In the Reflector 3 Preferences, if you have "Show Client Name" set to "Always" or "Hover", you will see the option to start recording at the top of the mirrored image on your computer.
You can also record from the Reflector 3 menu. Once your device is connected, simply open the Reflector 3 menu and press record.
You can also use key commands to begin recording.
Press Command and R to begin or end a recording.