For hypersonic inlets, buzz is a self-sustained oscillatory flow characterised by strong nonlinear and unsteady behaviour. Our recent study shows that, unlike conventional alterations in flow conditions at the inlet entrance or exit, flexible lip deformation is a newly identified trigger for buzz. However, the mechanism by which this fluid–structure interaction (FSI) behaviour induces buzz remains unclear. To clarify how FSI acts as a dominant factor in triggering flow instability leading to buzz, this study investigates a more general flexible plate model within the inlet. The results show that the plate FSI introduces a prolonged instability accumulation process for buzz evolution, resulting in a ‘gradual-onset’ characteristic differing from previous studies. During this process, plate FSI amplifies downstream flow oscillations while accumulating unstable energy. Eventually, the excessive unstable energy causes the shock train to destabilise and be disgorged from the inlet, initiating a complete instability process dominated by buzz. Notably, buzz induced by plate FSI exhibits unsteady characteristics similar to those observed in rigid inlets. Therefore, as an internal self-excited disturbance source, plate FSI produces relatively weaker disturbances than conventional flow modifications, but exhibits highly persistent accumulation effects and distinct multistage characteristics. This study reveals the buzz evolution mechanism under plate FSI, providing new insights into flow instability in hypersonic inlets.