Flow batteries are a promising technology for large scale energy storage and load balancing from intermittent power sources, but their viability hinges on our ability to attain high-power outputs while minimizing costs and meeting performance constraints. Effective engineering of these systems is further complicated by limitations on the control of the electrochemical cell component morphologies across scales. At Lawrence Livermore National Lab, we have pioneered a potential solution to this problem using additive manufacturing techniques which enable hierarchical structures controlled from the sub-micron through the centimeter length scales. Yet, even with this expanded design space, the complexity and tight coupling of the underlying physical processes remains as an obstacle to effective design: Apparently obvious choices can nevertheless lead to an unexpected adverse performance impact. To address this challenge, we present an automatic design methodology to optimize the electrode topology over precisely defined performance criteria. We combine forward physics solvers for the full electrochemical problem with gradient optimization code to optimize over multiple objectives simultaneously (e.g., maximizing current, minimizing pressure drop, minimizing material usage, etc.). Our algorithms compute optimal electrochemical cell geometries which are then physically manufactured using additive manufacturing techniques (e.g., direct ink write and projection micro-stereo lithography) and post-processed to create carbon electrodes. We compare the predicted performance of the designs against the experimentally measured performance of the manufactured devices. Our work provides a systematic path toward rational design of cost-effective, high-power flow batteries.