In recent years, efforts to assess the evolving risks of coastal compound surge and rainfall-driven flooding from tropical cyclones (TCs) and extratropical cyclones (ETCs) in a warming climate have intensified. While substantial progress has been made, the persistent challenge lies in obtaining actionable insights into the changing magnitude and spatially-varying flood risks in coastal areas. We employ a physics-based numerical hydrodynamic framework to simulate compound flooding from TCs and ETCs in both current and future warming climate conditions, focusing on the western side of Buzzard Bay in Massachusetts. Our approach leverages hydrodynamic models driven by extensive sets of synthetic TCs downscaled from CMIP6 climate models and dynamically downscaled ETC events using the WRF model forced by CMIP5 simulations. Through this methodology, we quantify the extent to which climate change can potentially reshape the risk landscape of compound flooding in the study area. Our findings reveal a significant increase in TC-induced compound flooding risk due to evolving climatology and sea level rise (SLR). Additionally, there is a heightened magnitude of compound flooding from ETCs, in coastal regions, due to SLR. Inland areas exhibit a decline in rainfall-driven flooding from high-frequency ETC events toward the end of the century compared to the current climate. Our methodology is transferable to other vulnerable coastal regions, serving as a valuable decision-making tool for adaptive measures in densely populated areas. It equips decision-makers and stakeholders with the means to effectively mitigate the destructive impacts of compound flooding arising from both current and future TCs and ETCs.