The effects of flow topology on the subgrid-scale (SGS) kinetic energy flux in compressible isotropic turbulence is studied. The eight flow topological types based on the three invariants of the filtered velocity gradient tensor are analysed at different scales, along with their roles in the magnitude and direction of kinetic energy transfer. The unstable focus/compressing (UFC), unstable node/saddle/saddle (UN/S/S) and stable focus/stretching (SFS), are the three predominant topological types at all scales; they account for at least 75 % of the flow domain. The UN/S/S and SFS types make major contributions to the average SGS flux of the kinetic energy from large scales to small scales in the inertial range. The unstable focus/stretching (UFS) topology makes a contribution to the reverse SGS flux of kinetic energy from small scales to large scales. In strong compression regions, the average contribution of the stable node/saddle/saddle (SN/S/S) topology to the SGS kinetic energy flux is positive and is predominant over those of other flow topologies. In strong expansion regions, the UFS topology makes a major contribution to the reverse SGS flux of the kinetic energy. As the turbulent Mach number increases, the increase of volume fraction of the UFS topological regions leads to the increase of the SGS backscatter of kinetic energy. The SN/S/S topology makes a dominant contribution to the direct SGS flux of the compressible component of the kinetic energy, while the UFS topology makes a dominant contribution to the reverse SGS flux of the compressible component of the kinetic energy.