A versatile video depth estimation model should be consistent and accurate across frames, produce high-resolution depth maps, and support real-time streaming. We propose a method, FlashDepth, that satisfies all three requirements, performing depth estimation for a 2044x1148 streaming video at 24 FPS. We show that, with careful modifications to pretrained single-image depth models, these capabilities are enabled with relatively little data and training. We validate our approach across multiple unseen datasets against state-of-the-art depth models, and find that our method outperforms them in terms of boundary sharpness and speed by a significant margin, while maintaining competitive accuracy. We hope our model will enable various applications that require high-resolution depth, such as visual effects editing, and online decision-making, such as robotics.