In this paper, a 10-gram Flapping-Wings Aerial Vehicle (FWAV) is demonstrated to perform the automatic trajectory tracking task based on a vector fields method. In this regard, the reference for the heading control is provided by a vector field which is computed according to the desired trajectory. The FWAV is endowed with a directional mechanism which permits to exert the directional control command simultaneously by tensing one wing and relaxing the opposite wing and by moving the rudder in the same direction. Due to the complex phenomena involved in the dynamics, a set of dedicated free flight tests was performed to identify a simplified linear model using system identification in order to adjust the yaw controller and the roll inner loop controller avoiding stall. Our experimental results proved that our time-independent vector field-based strategy enlarges the initial conditions spectra in which stability is observed over tens of meters. The tracking of circular and 8-shaped trajectories was successfully accomplished.