Urban flooding is a recurring and distressing issue with severe consequences, including the destruction of densely populated infrastructure and loss of life. Mapping inundated urban areas using synthetic aperture radar (SAR) data is crucial for local authorities to quickly assess risks and coordinate rescue efforts. However, due to the complexity of backscattering mechanisms, SAR-based urban floodwater mapping remains a challenge. In this work, we address this problem by introducing a novel algorithm, coherence-guided change transformer (CC-Former), for urban flood mapping that leverages the coherence of interferometric SAR (InSAR) with vision transformers. Specifically, CC-Former utilizes two Siamese weight-sharing encoders to extract multi-scale features from input InSAR coherence images and employs a decoder to generate final predictions. Additionally, we propose a coherence-based scaling (CoBS) module designed to focus on the acquired coherence features of urban flood classes and mitigate the imbalanced distribution of training classes. For qualitative and quantitative evaluation, the proposed CC-Former model was trained and validated using multi-temporal, dual-polarized Sentinel-1 SAR data to map the flood extent in Derna, Libya, following Tropical Storm Daniel in September 2023. Experimental results demonstrate that the proposed model outperforms state-of-the-art methods, achieving an F1 score of 89.4% and an IoU of 84.4% in both co- and cross-polarization, and an F1 score of 87.9% when integrating intensity and coherence. We conclude that the CC-Former model offers a promising solution for accurate and efficient urban flood mapping from InSAR coherence, with the potential for rapid generalization to other affected areas. As such, it can significantly aid disaster management efforts in vulnerable communities in near real-time.