Drawing inspiration from insect flapping wings, a Flapping Wing Rotor (FWR) has been developed for Micro Aerial Vehicle (MAV) applications. The FWR features unique active flapping and passive rotary kinematics of motion to achieve a high lift coefficient and flight efficiency. This study thoroughly investigates the aerodynamic performance and design of a bio-inspired flexible wing for FWR-MAVs, emphasizing its novel backward-curved wingtip and variable spanwise stiffness resembling a dragonfly's wing. The research departs from previous aerodynamic studies of FWR, which focused predominantly on rectangular and rigid wings, and delves into wing flexibility. Employing Computational Fluid Dynamics (CFD), Computational Structural Dynamics (CSD), and experimental measurements, the study demonstrates the aerodynamic benefits of the dragonfly-inspired FWR wingtip shape and its reinforced structure. Fluid-Structure Interaction (FSI) analysis is used to examine the effects of elastic deformation encompassing twist and bending on aerodynamic forces. The results underscore the importance of bending deformation in enhancing lift and power efficiency and propose a method for analysing variable stiffness along the wingspan using a vortex delay mechanism that is induced by delayed flapping motion. By comparing modelled and measured stiffness, the study validates the flexibility of the FWR wing, revealing optimal aerodynamic efficiency is achieved through moderate flexibility and spanwise stiffness variation. The curving leading-edge beam forming the sweep-back wingtip offers a practical approach to obtaining variable stiffness and aerodynamic benefits for FWR-MAVs. Using the same pair of dragonfly-like flexible wings, FWR-MAVs have effectively exhibited VTOL and hovering flight capabilities, spanning from a 25-g single-motor drive model to a 51-g dual-motor drive model. This research provides valuable insights into flexible wing design for FWR-MAVs, leveraging biomimicry to improve flight efficiency.