Method 1

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.

Method 2

You can also record from the Reflector 3 menu. Once your device is connected, simply open the Reflector 3 menu and press record.

Method 3

You can also use key commands to begin recording. 

Mac: Press command + r to begin or end a recording.
Windows: alt + r to begin or end a recording.