Here we describe how a 10-gram Flapping-Wing Micro Aerial Vehicle (FWMAV) was able to perform an automatic trajectory tracking task based on a vector field method. In this study, the desired heading was provided by a vector field which was computed depending on the desired trajectory. The FWMAV's heading was changed by a rear steering mechanism. This rear mechanism simultaneously (i) tenses one wing and relaxes the opposite wing, and (ii) moves the rudder in the same direction as the wing is relaxed. Due to the complex dynamics, system identification methods were used to identify simple linear models using a set of dedicated free flight tests. This yaw and roll simple models help to adjust the yaw controller and the inner loop roll controller. The experimental results obtained here show that a time-independent vector field-based strategy is robust to various initial position and/or speed conditions. The task of tracking circular and 8-shaped trajectories was accomplished successfully over tens of meters.