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Biological flyers take the advantage of FSI to augment their propulsive efficiency by exploiting the coupling between the flexible wings and the surrounding unsteady flow-field. A proper understanding of the role of FSI in natural flights is essential for the design of biologically-inspired Micro Aerial Vehicles (MAVs). In field conditions, the flow is typically accompanied by irregular fluctuations which significantly affect the performance of very light weight flapping wing MAVs, that are primarily aimed for indoor applications. The present study focusses on carrying out a stochastic bifurcation analysis to understand the effects of fluctuating flow on the dynamical stability characteristics of the coupled dynamical system. In this study, a span-wise flexible wing has been modelled by an elastically mounted airfoil supported by translational and rotational cubic nonlinear springs along the plunge (bending) and pitch (torsion) degrees of freedom respectively. The nonlinear structural model has been coupled with an inviscid flow solver using a weak coupling strategy to build the FSI framework. The flow part is solved using the unsteady vortex lattice method (UVLM). A bifurcation analysis has been carried out considering the mean wind speed to be the bifurcation parameter. In sterile flow conditions, the system undergoes a Hopf bifurcation as the free-stream velocity is increased resulting in stable limit-cycle oscillation (LCO) from a fixed point response. However, when long time scale gusts are superimposed to the mean flow, the dynamics of the system undergoes qualitative changes with the appearance of an intermittency regime prior to the onset of noisy LCOs. A P-bifurcation analysis based on the transition in the topology associated with the structure of the joint pdf of the response variables reveals that the joint pdf corresponding to the stochastic fixed point response (Fig. 1(a)) possesses a Dirac delta function like structure with a sharp single peak around zero at low mean wind speed. As the mean wind speed increased, one can see in the joint pdf that along with the peak around zero value, a new weak attractor is born (Fig. 1(b)). In this regime, the system experiences on-off intermittency. As the mean wind speed is further increased, the joint pdf bifurcates to a crater-like structure corresponding to the random LCO (Fig. 1(c)). The present paper further focusses on the stochastic bifurcations of the coupled system in the post-flutter regime in the presence of an actuating force the details of which will be presented in the full paper.