EMG-based gesture recognition shows promise for human-machine interaction. Systems are often afflicted by signal and electrode variability which degrades performance over time. We present an end-to-end system combating this variability using a large-area, high-density sensor array and a robust classification algorithm. EMG electrodes are fabricated on a flexible substrate and interfaced to a custom wireless device for 64-channel signal acquisition and streaming. We use brain-inspired high-dimensional (HD) computing for processing EMG features in one-shot learning. The HD algorithm is tolerant to noise and electrode misplacement and can quickly learn from few gestures without gradient descent or back-propagation. We achieve an average classification accuracy of 96.64% for five gestures, with only 7% degradation when training and testing across different days. Our system maintains this accuracy when trained with only three trials of gestures; it also demonstrates comparable accuracy with the state-of-the-art when trained with one trial.