Many industries extensively use flexible materials. Effective approaches for handling flexible objects with a robot manipulator must address residual vibrations. Existing solutions rely on complex models, use additional instrumentation for sensing the vibrations, or do not exploit the repetitive nature of most industrial tasks. This paper develops an iterative learning control approach that jointly learns model parameters and residual dynamics using only the interoceptive sensors of the robot. The learned model is subsequently utilized to design optimal (PTP) trajectories that accounts for residual vibration, nonlinear kinematics of the manipulator and joint limits. We experimentally show that the proposed approach reduces the residual vibrations by an order of magnitude compared with optimal vibration suppression using the analytical model and threefold compared with the available state-of-the-art method. These results demonstrate that effective handling of a flexible object does not require neither complex models nor additional instrumentation.