Musculoskeletal robots provide superior advantages in flexibility and dexterity, positioning them as a promising frontier towards embodied intelligence. However, current research is largely confined to relative simple tasks, restricting the exploration of their full potential in multi-segment coordination. Furthermore, efficient learning remains a challenge, primarily due to the high-dimensional action space and inherent overactuated structures. To address these challenges, we propose Diff-Muscle, a musculoskeletal robot control algorithm that leverages differential flatness to reformulate policy learning from the redundant muscle-activation space into a significantly lower-dimensional joint space. Furthermore, we utilize the highly dynamic robotic table tennis task to evaluate our algorithm. Specifically, we propose a hierarchical reinforcement learning framework that integrates a Kinematics-based Muscle Actuation Controller (K-MAC) with high-level trajectory planning, enabling a musculoskeletal robot to perform dexterous and precise rallies. Experimental results demonstrate that Diff-Muscle significantly outperforms state-of-the-art baselines in success rates while maintaining minimal muscle activation. Notably, the proposed framework successfully enables the musculoskeletal robots to achieve continuous rallies in a challenging dual-robot setting.