Significant amount of research interest is focused on the development of nature-inspired Micro Areal Vehicle (MAV) due to their multifold potential in the futuristic civil and military applications over the years. Natural flyers (bird/insect) employ several flapping mechanisms to undergo complicated aerial manoeuver efficiently. The bistable “click” mechanism is one of the most popular modelling approaches for representing the muscle–wing interactions in the insect flight motor during Dipteran flight. The kinetic energy of the wing is stored as elastic energy while deforming the muscle elements in the flight motor during one stroke of flapping and gets recovered in the reverse stroke. The present work investigates the non-linear Fluid–Structure Interaction (FSI) of a Dipteran flight motor-inspired flapping system with the surrounding free stream at low Reynolds number. The FSI effects of the Dipteran wing assimilated as a forced Duffing oscillator model to gain a deep understanding of the non-linear dynamical behaviour of the system in the presence of aerodynamic loads. The aerodynamic loads on the wing are computed using a discrete forcing Immersed Boundary Method (IBM)-based in-house Navier–Stokes solver. The structural governing equation is solved using an explicit fourth-order Runge–Kutta (RK4) method and is coupled with the IBM solver through a weak coupling scheme. Dynamical time-series analysis tools have been employed to study the non-linear behaviour of the combined FSI system. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.