Supercritical fluids (SCFs) are widely utilized in advanced energy systems due to their exceptional heat transfer characteristics. However, flow instability, particularly near pseudo-critical conditions, poses a significant challenge to their effective applications. Despite extensive research, the coupled effects of thermal and fluid dynamic mechanisms on flow instability remain insufficiently understood, particularly in supercritical water (SCW) systems. This study identifies the onset of flow instability (OFI) in the negative slope region of pressure drop curve during steady-state conditions, analyzing the relationship between pressure drop and mass flow rate. Transient analyses were then conducted to investigate the influence of operating parameters on oscillatory phenomena such as pressure drop oscillations (PDO), density wave oscillations (DWO), and thermal oscillations (ThO). The results show that higher mass flow rates and heat fluxes, reduce pressure oscillations by up to 20% and stabilize temperature fluctuations, minimizing thermal-fluid coupling effects. Conversely, lower mass flow rates and moderate heat flux increase these oscillations amplitudes, with pressure oscillations decreasing by 20% and temperature oscillations increasing by 14.29%, due to stronger interactions between thermal expansion, compressibility, and density variations near pseudo critical conditions. At 27MPa, flow instability increases as mass flow rates decrease, while at 25MPa with varying inlet temperatures, enhanced coupling effects were observed under similar operating conditions. These findings highlight the sensitivity of SCW flow stability to operating parameters, providing crucial insights for optimizing thermal system performance in supercritical applications such as power generation, heat exchangers, and advanced cooling technologies. This robust methodology not only advances our understanding of SCFs behavior but also paves the way for optimizing stability and efficiency in next-generation energy systems.