Wind power (WP) penetration in weak distribution networks is associated with adverse impacts on voltage quality. The installation of an energy storage system (ESS) is a possible voltage quality remedy in such milieus. This paper proposes a supercapacitor ESS for alleviation of voltage flicker resulting from WP integration. The proposed ESS control and management are tailored to that purpose such that the ESS offsets the flicker-producing fluctuations in the generated WP. The proposed power sizing of the ESS is defined by the estimated turbulence intensity and wind speed average at the installation site. A 2 MW wind generator of the doubly fed induction generator type is employed as a source of WP and simulations are conducted on a simplified test system, as well as a detailed 25 kV distribution network on which results are compared with acknowledged reactive power flicker mitigation approaches and verified by prototyping in a real-time simulation platform. The flicker measurement procedure is conducted per IEC Standard 61000-4-15.