Due to the harsh and unknown underwater environment, the question of how autonomous underwater vehicles (AUVs) should navigate and maneuver, especially in a dynamic environment with changing flow patterns, is still largely open. This paper presents a systematic background flow sensing framework, which plays an important role in improving the navigation/control intelligence of AUVs. This flow sensing framework utilizes distributed pressure measurements of AUVs to estimate surrounding flow fields. The proposed method first determines the flow pattern/model around AUVs based on fast Fourier transform (FFT) spectrum analysis and then uses recursive Bayesian estimation and dynamic mode decomposition (DMD)-based modeling to identify model parameters. This method is capable of sensing background flow fields even in flow pattern changing environments, e.g., open waters in real-world scenarios, thus dramatically expanding the application scope of the existing flow sensing methods. Simulation results are provided to demonstrate the effectiveness of the proposed flow sensing method.