A flat band in fermionic system is a dispersionless single-particle state with a diverging effective mass and nearly zero group velocity. These flat bands are expected to support exotic properties in the ground state, which might be important for a wide range of promising physical phenomena. For many applications, it is highly desirable to have such states in Dirac materials, but so far they have been reported only in some nonmagnetic Dirac systems. In this paper, we propose a realization of topologically protected spin-polarized flat bands generated by domain walls in planar magnetic topological insulators. Using first-principles material design, we suggest a family of intrinsic antiferromagnetic topological insulators with an in-plane sublattice magnetization and high Neel temperature. Such systems can host domain walls in a natural manner. For these materials, we demonstrate the existence of spin-polarized flat bands in the vicinity of the Fermi level and discuss their properties and potential applications.