Motivated by the requirement for developing a lightweight and nimble underwater vehicle-manipulator system (UVMS), this paper presents a novel design of the overall framework and the functional modules for a flippers-driven UVMS (F-UVMS), which is equipped with 6 biomimetic flipper propulsors to produce thrust. With taking into account the material properties and flexible deformation, the dynamic model of the flexible flipper is derived. The fluid-solid coupling analysis reveals the wake vorticity characteristics and the mechanism of the flexible flipper. Besides, by introducing the dimensionless swimming number Sw, the force-parameter relationship of the flexible flipper is revealed. By comparing the hydrodynamic characteristics of the flexible flipper and rigid flipper, it can be concluded that the flexible flipper has higher propulsion efficiency. The motion patterns of the F-UVMS are designed by proposed coordinated control strategy. Moreover, through computational fluid dynamics method, the hydrodynamic effects of the biomimetic flipper propulsors during forward motion are analyzed. Finally, the force measurement experiments and the thrust efficiency experiments validate the practicability of the proposed biomimetic flipper propulsor. The motion feasibility of the F-UVMS is verified by the motion experiments.