Two-dimensional materials with high charge carrier mobility and tunable band gaps have attracted intense research effort for their potential use in nanoelectronics. Two-dimensional ?-conjugated polymers constitute a promising subclass because the band structure can be manipulated by varying the molecular building blocks while preserving key features such as Dirac cones and high charge mobility. The major barriers to the application of two-dimensional ?-conjugated polymers have been the small domain size and high defect density attained in the syntheses explored so far. Here, we demonstrate the fabrication of mesoscale ordered two-dimensional ?-conjugated polymer kagome lattices with semiconducting properties, Dirac cone structures and flat bands on Au(111). This material has been obtained by combining a rigid azatriangulene precursor and a hot dosing approach, which favours molecular diffusion and eliminates voids in the network. These results open opportunities for the synthesis of two-dimensional ?-conjugated polymer Dirac cone materials and their integration into devices.