  We study the appearance of topological Floquet flat bands in
alternating-twist multilayer graphene, which has alternating relative twist
angle $\pm\theta$ near the first magic angle. While the system hosts both flat
bands and a steep Dirac cone in the static case, the circularly polarized laser
beam can open a gap at the Moir\'{e} $K$ point and create Floquet flat bands
carrying nonzero Chern numbers. Considering recent lattice-relaxation results,
we find that the topological flat band is well-isolated for the effective
interlayer tunneling in $n=3, 4, 5$ layers. Such dynamically produced
topological flat bands are potentially observed in the experiment and thus
provide a feasible way to realize the fractional Chern insulator.
