In this paper we exploit a novel identification algorithm to identify a linear parameter-varying (LPV) aeroelastic system equipped with trailing edge flaps. In the identification algorithm we use a recently introduced factorization which makes it possible to form predictors which are based on past inputs, outputs, and known aeroelastic data. The predictors contain the LPV equivalent of the Markov parameters. Using the predictors, ideas from Predictor Based Subspace IDentification (PBSID) are developed to estimate the state sequence from which the LPV aeroelastic system matrices can be constructed. Since the algorithm can be used in a closed-loop setting it can be applied on a flutter example.