Federated learning (FL) enables distributed clients to collaboratively train a global model using local private data. Nevertheless, recent studies show that conventional FL algorithms still exhibit deficiencies in privacy protection, and the server lacks a reliable and stable aggregation rule for updating the global model. This situation creates opportunities for adversaries: on the one hand, they may eavesdrop on uploaded gradients or model parameters, potentially leaking benign clients' private data; on the other hand, they may compromise clients to launch poisoning attacks that corrupt the global model. To balance accuracy and security, we propose FedFG, a robust FL framework based on flow-matching generation that simultaneously preserves client privacy and resists sophisticated poisoning attacks. On the client side, each local network is decoupled into a private feature extractor and a public classifier. Each client is further equipped with a flow-matching generator that replaces the extractor when interacting with the server, thereby protecting private features while learning an approximation of the underlying data distribution. Complementing the client-side design, the server employs a client-update verification scheme and a novel robust aggregation mechanism driven by synthetic samples produced by the flow-matching generator. Experiments on MNIST, FMNIST, and CIFAR-10 demonstrate that, compared with prior work, our approach adapts to multiple attack strategies and achieves higher accuracy while maintaining strong privacy protection.