Electronic skin (e-skin) is playing an increasingly important role in health detection, robotic teleoperation, and human-machine interaction, but most e-skins currently lack the integration of on-site signal acquisition and transmission modules. In this paper, we develop a novel flexible wearable e-skin sensing system with 11 sensing channels for robotic teleoperation. The designed sensing system is mainly composed of three components: e-skin sensor, customized flexible printed circuit (FPC), and human-machine interface. The e-skin sensor has 10 stretchable resistors distributed at the proximal and metacarpal joints of each finger respectively and 1 stretchable resistor distributed at the purlicue. The e-skin sensor can be attached to the opisthenar, and thanks to its stretchability, the sensor can detect the bent angle of the finger. The customized FPC, with WiFi module, wirelessly transmits the signal to the terminal device with human-machine interface, and we design a graphical user interface based on the Qt framework for real-time signal acquisition, storage, and display. Based on this developed e-skin system and self-developed robotic multi-fingered hand, we conduct gesture recognition and robotic multi-fingered teleoperation experiments using deep learning techniques and obtain a recognition accuracy of 91.22%. The results demonstrate that the developed e-skin sensing system has great potential in human-machine interaction.