Urban flooding in arid regions poses severe risks to infrastructure and communities. Accurate, fine-scale mapping of flood extents and recovery trajectories is therefore essential for improving emergency response and resilience planning. However, arid environments often exhibit limited spectral contrast between water and adjacent surfaces, rapid hydrological dynamics, and highly heterogeneous urban land covers, which challenge traditional flood-mapping approaches. High-resolution, daily PlanetScope imagery provides the temporal and spatial detail needed. In this work, we introduce FM-LC, a hierarchical framework for Flood Mapping by Land Cover identification, for this challenging task. Through a three-stage process, it first uses an initial multi-class U-Net to segment imagery into water, vegetation, built area, and bare ground classes. We identify that this method has confusion between spectrally similar categories (e.g., water vs. vegetation). Second, by early checking, the class with the major misclassified area is flagged, and a lightweight binary expert segmentation model is trained to distinguish the flagged class from the rest. Third, a Bayesian smoothing step refines boundaries and removes spurious noise by leveraging nearby pixel information. We validate the framework on the April 2024 Dubai storm event, using pre- and post-rainfall PlanetScope composites. Experimental results demonstrate average F1-score improvements of up to 29% across all land-cover classes and notably sharper flood delineations, significantly outperforming conventional single-stage U-Net baselines.