Reflective flare is a phenomenon that occurs when light reflects inside lenses, causing bright spots or a ''ghosting effect'' in photos, which can impact their quality. Eliminating reflective flare is highly desirable but challenging. Many existing methods rely on manually designed features to detect these bright spots, but they often fail to identify reflective flares created by various types of light and may even mistakenly remove the light sources in scenarios with multiple light sources. To address these challenges, we propose an optical center symmetry prior, which suggests that the reflective flare and light source are always symmetrical around the lens's optical center. This prior helps to locate the reflective flare's proposal region more accurately and can be applied to most smartphone cameras. Building on this prior, we create the first reflective flare removal dataset called BracketFlare, which contains diverse and realistic reflective flare patterns. We use continuous bracketing to capture the reflective flare pattern in the underexposed image and combine it with a normally exposed image to synthesize a pair of flare-corrupted and flare-free images. With the dataset, neural networks can be trained to remove the reflective flares effectively. Extensive experiments demonstrate the effectiveness of our method on both synthetic and real-world datasets.