The flow angles such as the angle of attack and the angle of slip are the important air data for the aircraft. For the present advanced aircraft, the flush air data sensing (FADS) system is widely used and the artificial neural network is one of the important methods to estimate the air data for FADS. However, the most present ANNs for FADS are more prefer to fit the relationship in the mathematical sense within the training set and the physical and geometric senses are easy to ignore. That makes the estimation accuracy of the ANN strongly limited with the amount and the range of the training set. In this paper, a new flow angle estimation ANN is proposed. Which is decoupled from the pressure parameters estimation such as static and dynamic pressure by the surface pressure distribution model analysis. The input of this method is constrained by this model to eliminate the influence of the pressure parameters. Two different experiments are designed based on the wind tunnel experiment data to verify the performances of the method in different aspects. The results show that, by the new method, when the training set could cover the test set, the maximum error of angle of attack and angle of slip estimation is less than 0.12°. When the test set is out of the training set’s range, the maximum error for the above estimation could be limited below 1°.