Synchrotron radiation facilities generate ultra-high-speed diffraction image data streams, which require data screening to reduce the pressure on data transmission and storage. However, competing research groups are reluctant to share such data, and existing deep learning-based screening methods cannot easily achieve effective training under privacy protection. Therefore, for the first time, this study applies the federated learning technology to the screening of radiation source diffraction images, and training data augmentation under privacy protection is realized by separating the data and the model. The Federated Kullback-Leibler (FedKL) screening method is also proposed to improve the global model update based on Kullback-Leibler divergence and data volume weights, thus reducing the complexity of the algorithm while obtaining high accuracy; further, this satisfies the high-precision processing requirements for high-speed data streams. To address the difficulties encountered in data synchronization training for multiple centers of remote light sources, this paper also proposes a hybrid training method that combines the synchronous and asynchronous approaches; this significantly improves the training speed of the model without reducing the recognition accuracy. Experiments on the light source CXIDB-76 public dataset reveal that FedKL can improve the accuracy and F1 score by 25.2 percentage points and 0.419, respectively, compared with FedAvg.