We present the design of a flexible multilayer circuit board for use in a custom-built microwave system for breast health monitoring. The flexible circuit features both an integrated solid-state switching network and 16 wideband antennas, which transmit short-duration pulses into the breast tissues and receive the backscattered responses. By integrating the switching matrix and the antenna array on the same substrate, we reduce the overall cost and size of the system in comparison with previously demonstrated systems in the literature. We characterize the performance of the flexible circuit board using our clinically tested experimental system and demonstrate its functionality through successful imaging of dielectrically realistic breast phantoms that simulate the presence of a tumor. This represents a step toward a more patient-friendly, compact, cost-effective, and wearable design in contrast to previous systems in the literature that required a clinical table or used bulky rigid antenna housings and electromechanical switching networks.