Wind tunnel testing of large deformable soft kites for wind energy conversion is practically not feasible. Computational simulation of the coupled fluid-structure interaction problem is scientifically challenging and of limited practical use for aerodynamic characterization. In this paper we present a novel experimental method for aerodynamic characterization of flexible membrane kites by in situ measurement of the relative flow, while performing complex flight maneuvers. We find that the measured aerodynamic coefficients agree well with the values that are currently used for flight simulation of soft kites. For flight operation in crosswind maneuvers where the traction force is kept constant, the angle of attack and the apparent flow velocity exhibit opposite trends. For entire pumping cycles, the measurements show considerable variations of the aerodynamic coefficients, while the angle of attack of the kite varies in fact only in a narrow range. This finding questions the commonly used representation of aerodynamic coefficients as sole functions of the angle of attack and stresses the importance of aeroelastic deformation for this type of wing. Considering the effect of the power setting (identical to the trim) solely as a rigid-body pitch rotation does not adequately describe the aero-structural behavior of the kite. We show that the aerodynamic coefficients vary as functions of the power setting (trim) of the kite, the steering commands and flight direction.