The increasing frequency and intensity of extreme weather events make flood risk management a critical challenge for cities worldwide, particularly in the current context of climate change. This work presents a cloud-based methodological framework for the semi-automated analysis of urban and peri-urban flood dynamics using remote sensing data. The methodology leverages the computational power of Google Earth Engine (GEE) to process Synthetic Aperture Radar (SAR) data from Sentinel-1 and optical imagery from Sentinel-2, along with auxiliary hydro-meteorological data. A classification scheme based on fuzzy logic is employed to improve the accuracy of flood detection, especially in complex environments with vegetation cover. To facilitate its practical application by urban managers, the algorithm has been implemented in an interactive WebGIS platform, conceived as a tool for smart governance and emergency management. The framework's effectiveness was validated using the catastrophic flood event caused by a cut-off low (DANA) in Valencia (Spain) in October 2024 as a case study. The results represent a valuable contribution to the development of smart public services, offering a scalable and accessible solution to improve urban resilience against hydro-meteorological risks.