The electrochemical flow capacitor (EFC) has been recently introduced as a new concept for rapid and capacitive energy storage using flowable carbon-electrolyte suspensions. In our study, we investigate the EFC under static and constant flow condition. Unlike static carbon suspensions where poor particle-particle-contact and particle settling yield a highly resistive and time-dependent behavior, we show that flow operation of carbon suspensions reach high Coulombic efficiency and stable energy density performance. Our results also indicate that the specific capacitance per total mass of carbon electrodes in flow operation is comparable to conventional binder-bound carbon film electrodes.