In this paper, we present mmFlux: a novel framework for extracting underlying crowd motion patterns and inferring crowd semantics using mmWave radar. First, our proposed signal processing pipeline combines optical flow estimation concepts from vision with novel statistical and morphological noise filtering. This approach generates high-fidelity mmWave flow fields-compact 2D vector representations of crowd motion. We then introduce a novel approach that transforms these fields into directed geometric graphs. In these graphs, edges capture dominant flow currents, vertices mark crowd splitting or merging, and flow distribution is quantified across edges. Finally, we show that analyzing the local Jacobian and computing the corresponding curl and divergence enables extraction of key crowd semantics for both structured and diffused crowds. We conduct 21 experiments on crowds of up to 20 people across 3 areas, using commodity mmWave radar. Our framework achieves high-fidelity graph reconstruction of the underlying flow structure, even for complex crowd patterns, demonstrating strong spatial alignment and precise quantitative characterization of flow split ratios. Finally, our curl and divergence analysis accurately infers key crowd semantics, e.g., abrupt turns, boundaries where flow directions shift, dispersions, and gatherings. Overall, these findings validate mmFlux, underscoring its potential for various crowd analytics applications.