Predicting the future occupancy of the surrounding environment is a vital task for autonomous driving. However, current best-performing single-modality or multi-modality fusion methods can only predict uniform snapshots of future occupancy states and still require strictly synchronous sensory data for sensor fusion. We propose a StreamingFlow framework to lift these strong limitations. StreamingFlow is a novel BEV occupancy predictor that ingests asynchronous multi-sensor data streams for fusion and performs streaming forecasting of the future occupancy map at any future timestamps. By integrating neural ordinary differential equations (N-ODE) onto recurrent neural networks, StreamingFlow learns derivatives of BEV features over temporal horizons, updates the implicit sensor's BEV feature as part of the fusion process, and propagates BEV states to the desired future time point. Extensive experiments on two large-scale datasets, nuScenes and Lyft L5, demonstrate that StreamingFlow significantly outperforms previous vision-based, lidar-based methods, and shows competitive performance compared to state-of-the-art fusion-based methods with a much lighter model.