Electromyography (EMG)-based gesture recognition has emerged as a promising approach for human-computer interaction. However, its performance is often limited by the scarcity of labeled EMG data, significant cross-user variability, and poor generalization to unseen gestures. To address these challenges, we propose SeqEMG-GAN, a conditional, sequence-driven generative framework that synthesizes high-fidelity EMG signals from hand joint angle sequences. Our method introduces a context-aware architecture composed of an angle encoder, a dual-layer context encoder featuring the novel Ang2Gist unit, a deep convolutional EMG generator, and a discriminator, all jointly optimized via adversarial learning. By conditioning on joint kinematic trajectories, SeqEMG-GAN is capable of generating semantically consistent EMG sequences, even for previously unseen gestures, thereby enhancing data diversity and physiological plausibility. Experimental results show that classifiers trained solely on synthetic data experience only a slight accuracy drop (from 57.77% to 55.71%). In contrast, training with a combination of real and synthetic data significantly improves accuracy to 60.53%, outperforming real-only training by 2.76%. These findings demonstrate the effectiveness of our framework, also achieves the state-of-art performance in augmenting EMG datasets and enhancing gesture recognition performance for applications such as neural robotic hand control, AI/AR glasses, and gesture-based virtual gaming systems.