Singular flat band has potential in various fields, including condensed matter physics, materials science, and electronic device engineering. Here, we investigated the artificial formation of a singular flat band through the utilization of spoof plasmons and the subsequent calculation of its quantum distance. The band structure of spoof plasmons arises from the dispersion relation involving the momenta and polarization angle of the incident beam. We designed a metamaterial consisting of a gold structure shaped as a Kagome lattice on a polyimide substrate. Through transmission simulation in the terahertz regime, with varying incidence and azimuthal angles, the resulting band structure was observed. Analysis of the simulated transmission minima in momentum-frequency space revealed the presence of a flat band and a degenerate quadratic band originating from the zero point. Confirmation of the singularity and calculation of the associated quantum distance could be achieved by analyzing the eigenvectors corresponding to the flat band.