In order to assess damage and properly allocate relief efforts, mapping the extent of flood events is a necessary and important aspect of disaster management. In recent years, deep learning methods have evolved as an effective tool to quickly label high-resolution imagery and provide necessary flood extent mappings. These methods, though, require large amounts of annotated training data to create models that are accurate and robust to new flooded imagery. In this work, we provide FloodTrace, an application that enables effective crowdsourcing for flooded region annotation for machine learning training data, removing the requirement for annotation to be done solely by researchers. We accomplish this through two orthogonal methods within our application, informed by requirements from domain experts. First, we utilize elevation-guided annotation tools and 3D rendering to inform user annotation decisions with digital elevation model data, improving annotation accuracy. For this purpose, we provide a unique annotation method that uses topological data analysis to outperform the state-of-the-art elevation-guided annotation tool in efficiency. Second, we provide a framework for researchers to review aggregated crowdsourced annotations and correct inaccuracies using methods inspired by uncertainty visualization. We conducted a user study to confirm the application effectiveness in which 266 graduate students annotated high-resolution aerial imagery from Hurricane Matthew in North Carolina. Experimental results show the accuracy and efficiency benefits of our application apply even for untrained users. In addition, using our aggregation and correction framework, flood detection models trained on crowdsourced annotations were able to achieve performance equal to models trained on expert-labeled annotations, while requiring a fraction of the time on the part of the researcher.