Flexible cameras are important early warning wearable devices to protect security personnel from dangerous events. However, the desired key component of flexible cameras, a highly-sensitive and high-response-speed flexible photodetector, is difficult to create using conventional inorganic semiconductors. Here, we propose a low-temperature synthesis method to grow perovskite nanoflakes with high flexibility and crystallinity on a polymeric substrate. Furthermore, a high-performance flexible photodetector based on the obtained perovskite nanoflakes was fabricated. Its photoresponsivity rivals the highest values reported and, simultaneously, its response speed is faster than those of most current flexible photodetectors by 1-3 orders of magnitude.