Flutter is one of the most important aeroelastic instability phenomena that arises from the interaction between the structural dynamics of the mechanical airfoil system and the surrounding airflow. This instability phenomenon can lead not only to a reduction in aircraft performance but also to catastrophic structural failure. Therefore, one of the major challenges is to perform parametric and sensitivity studies on the stability behavior of a wing system subject to many random uncertainties in order to achieve a thorough understanding and reliable estimation of the role played by each parameter in the flutter phenomenon. To carry out such a study, an advanced surrogate modeling technique based on kriging and polynomial chaos expansion (PCE) is proposed for the prediction of flutter instability. In addition, a methodology based on hybrid surrogate modeling with advanced automatic kriging construction is discussed to promote an efficient parametric study of the airfoil system with uncertainties subjected to flutter. The Sobol indices highlight that the role played by each random parameter depends strongly on the flow speed and airfoil geometry with complex behaviors, giving valuable insights into the physics and the complexity of flutter.