Dual-arm cooperative manipulation holds great promise for tackling complex real-world tasks that demand seamless coordination and adaptive dynamics. Despite substantial progress in learning-based motion planning, most approaches struggle to generalize across diverse manipulation tasks and adapt to dynamic, unstructured environments, particularly in scenarios involving interactions between two objects such as assembly, tool use, and bimanual grasping. To address these challenges, we introduce a novel VLM-Assisted Siamese Flow Diffusion (VLM-SFD) framework for efficient imitation learning in dual-arm cooperative manipulation. The proposed VLM-SFD framework exhibits outstanding adaptability, significantly enhancing the ability to rapidly adapt and generalize to diverse real-world tasks from only a minimal number of human demonstrations. Specifically, we propose a Siamese Flow Diffusion Network (SFDNet) employs a dual-encoder-decoder Siamese architecture to embed two target objects into a shared latent space, while a diffusion-based conditioning process - conditioned by task instructions - generates two-stream object-centric motion flows that guide dual-arm coordination. We further design a dynamic task assignment strategy that seamlessly maps the predicted 2D motion flows into 3D space and incorporates a pre-trained vision-language model (VLM) to adaptively assign the optimal motion to each robotic arm over time. Experiments validate the effectiveness of the proposed method, demonstrating its ability to generalize to diverse manipulation tasks while maintaining high efficiency and adaptability. The code and demo videos are publicly available on our project website https://sites.google.com/view/vlm-sfd/.