The fast development of large language models (LLMs) and popularization of cloud computing have led to increasing concerns on privacy safeguarding and data security of cross-cloud model deployment and training as the key challenges. We present a new framework for addressing these issues along with enabling privacy preserving collaboration on training between distributed clouds based on federated learning. Our mechanism encompasses cutting-edge cryptographic primitives, dynamic model aggregation techniques, and cross-cloud data harmonization solutions to enhance security, efficiency, and scalability to the traditional federated learning paradigm. Furthermore, we proposed a hybrid aggregation scheme to mitigate the threat of Data Leakage and to optimize the aggregation of model updates, thus achieving substantial enhancement on the model effectiveness and stability. Experimental results demonstrate that the training efficiency, privacy protection, and model accuracy of the proposed model compare favorably to those of the traditional federated learning method.