Owing to its unique, concealment and easy customisation by combining different wrist and hand gestures, High-Density surface electromyogram (HD-sEMG) is recognised as a potential solution to the next generation biometric authentication, which usually adopts a wireless Body Sensor Network (BSN) to acquire the multi-channel HD-sEMG biosignals from distributed electrode arrays. For more accurate and reliable classification, biometric authentication requires the distributed biosignals to be sampled simultaneously and be well-aligned, which means that the sampling jitters among the arrays need to be tiny. To synchronise data sampling clocks of a cluster of BSN nodes for biometric authentication, this paper modifies the Packet-Coupled Oscillators protocol by using a Dynamic controller (D-PkCOs). This protocol only involves one-way single packet exchange, which reduces the communication overhead significantly. For the purpose of maintaining precise sampling of these BSN nodes subject to drifting clock frequency and varying delays, the dynamic controller is designed via the H∞ robust method, and it is proved that all the BSN nodes’ sampling jitters are bounded. The experimental results demonstrate that the D-PkCOs protocol can keep the sampling jitters less than a microsecond in a 10-node IEEE 802.15.4 network. The application of D-PkCOs to the BSN shows that the HD-sEMG signal with a high signal-to-noise ratio is obtained, which leads to better gesture classification performance.