Near-real time estimation of damage to buildings and infrastructure, referred to as damage nowcasting in this study, is crucial for empowering emergency responders to make informed decisions regarding evacuation orders and infrastructure repair priorities during disaster response and recovery. Here, we introduce FloodDamageCast, a machine learning framework tailored for property flood damage nowcasting. The framework leverages heterogeneous data to predict residential flood damage at a resolution of 500 meters by 500 meters within Harris County, Texas, during the 2017 Hurricane Harvey. To deal with data imbalance, FloodDamageCast incorporates a generative adversarial networks-based data augmentation coupled with an efficient machine learning model. The results demonstrate the model's ability to identify high-damage spatial areas that would be overlooked by baseline models. Insights gleaned from flood damage nowcasting can assist emergency responders to more efficiently identify repair needs, allocate resources, and streamline on-the-ground inspections, thereby saving both time and effort.