The interplay between scaffold geometry and mechanical cues is critical in regulating osteogenesis within engineered bone microenvironments. To better mimic native bone physiology and improve regeneration strategies, it is essential to integrate precise topological control with physiologically relevant flow. Here, a bone-on-a-chip (BoC) system coupled with triply periodic minimal surface (TPMS)–based 3D scaffolds is presented to investigate how geometric parameters—pore shape and solidity—govern osteogenic responses under dynamic perfusion. Using Gyroid and Schwarz diamond TPMS architectures, scaffolds with controlled pore geometries are created to modulate wall shear stress (WSS). Under flow conditions in the BoC system, pre-osteoblasts exhibit geometry-dependent behaviors in terms of infiltration, alkaline phosphatase activity, calcium deposition, and collagen formation. Scaffolds with intermediate solidity and curvature optimize WSS distribution and significantly enhance osteogenic differentiation. Additionally, a critical pore size threshold is identified beyond which flow-mediated signaling is attenuated, highlighting the importance of geometric precision. The results demonstrate the synergistic role of scaffold topology and interstitial flow in directing osteogenesis. This integrated platform provides a versatile tool for studying bone mechanobiology and offers a promising strategy for designing biomimetic scaffolds in regenerative medicine and bone tissue engineering.