Soft Robotics has applications in myriad fields from assistive wearables to autonomous exploration. Currently, the portability and performance of many devices is limited by their associated pneumatic energy source, requiring either large, heavy pressure vessels or noisy, inefficient air pumps. Here we present a lightweight, flexible, Electro-pneumatic Pump (EPP), which can silently control volume and pressure, enabling portable, local energy provision for Soft Robots, overcoming the limitations of existing pneumatic power sources. The EPP is actuated using dielectric-fluid-amplified electrostatic zipping, and the device presented here can exert pressures up to 2.34 kilopascals, deliver volumetric flow rates up to 161 millilitres per minute and under 0.5 watts of power, despite only having a thickness of 1.1 millimetres and weight of 5.3 grams. An EPP was able to drive a typical Soft Robotic actuator to achieve a maximum contraction change of 32.40% and actuation velocity of 54.43% per second. We highlight the versatility of this technology by presenting three EPP-driven embodiments: an antagonistic mechanism, an arm-flexing wearable robotic device, and a continuous-pumping system. This work shows the wide applicability of the EPP to enable advanced wearable assistive devices and lightweight, mobile, multifunctional robots.