And looking at the Gunship game, there is no ribbon. ...
http://battlelog.battlefield.com/bf4...800/171384095/

Thus, I would assume that you would need to achieve one of the following:
Scout Helicopter ribbon - Kill 5 enemies with a Scout helicopter
Attack Helicopter ribbon - Kill 5 enemies with an Attack helicopter
Jet Fighter ribbon - Kill 5 enemies with a Jet Fighter

I would suspect that the way for a non-pilot to earn this is in the Attack chopper gunner seat, though I have been interested in learning one of the Anti-Gravity Arts.