The permeability of CO2 sequestration is influenced by the characteristics of pore–fracture structures in coal, yet the flow simulation via the pore network model (PNM) and the controls of topology and morphology on permeability remain to be understood. First, the pore–fracture structure of high-volatile bituminous coal (HVBC) is characterized using micro-computed tomography, and the flow characteristics of single-phase CO2 in the connected pore–fracture network are simulated by the PNM. Second, the surface roughness of the connected pore–fracture is extracted by fractal characterization, and morphological algorithms are applied to accurately present the pore–fracture network structure. Finally, the implications of structural parameters (pore or throat diameter, coordination number, tortuosity, and sphericity) on CO2 transport are discussed, and the mechanism of pore–fracture structure response due to mineral dissolution in CO2 injection is analyzed. The results shows that the HVBC sample provides significant pore–fracture space (porosity of 10.87%) and flow path (connectivity of 66.50%) for hydrogen and carbon storage. CO2 flow simulation results demonstrate anisotropic flow, with higher CO2 permeability observed in the Z-axis direction (0.061 × 10−3 μm2) compared to the X- and Y-axis directions (0.044 × 10−3 μm2 and 0.059 × 10−3 μm2, respectively). Moreover, the fractures perpendicular to the coal bedding plane in the coal seam with a large tectonic dip strongly influence the flow of CO2 injection. Fractal analysis reveals a positive correlation between fractal dimension and porosity, indicating that structures with higher surface roughness are not convenient for CO2 transport. Significant pore angle characteristics (sphericity average of 0.58), high pore–throat connectivity (coordination number average of 4.31), and low capillary resistance (tortuosity average of 1.19) collectively affect the flow of CO2. Overall, the strongly anisotropic pore–fracture structure contributes to the inhomogeneous flow pattern in CO2 geosequestration. Changes in pore–fracture structure resulting from mineral dissolution during the early stage of CO2–coal matrix interaction in the HVBC reservoir can significantly enhance storage potential. This study contributes to the existing understanding of flow characteristics and provides insights for optimizing CO2 injection efficiency in carbon geosequestration.