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Modern mmWave systems have limited scalability due to inflexibility in performing frequency multiplexing. All the frequency components in the signal are beamformed to one direction via pencil beams and cannot be streamed to other user directions. We present a new flexible mmWave system called mmFlexible, which enables flexible directional frequency multiplexing. In this system, different frequency components of the mmWave signal are beamformed in multiple arbitrary directions with the same pencil beam. Our system makes two key contributions: (1) We propose a novel mmWave front-end architecture, called a delay-phased array, that utilizes a variable delay and variable phase element to create the desired frequency-direction response. (2) We propose a novel algorithm called FSDA (Frequency-space to delay-antenna) to estimate delay and phase values for the real-time operation of the delay-phased array. Through evaluations using mmWave channel traces, we demonstrate that mmFlexible achieves a 60-150% reduction in worst-case latency compared to the baselines.