  Twisted bilayer graphene (TBG) near "magic angles" has emerged as a rich
platform for strongly correlated states of two-dimensional Dirac semimetals.
Here we show that twisted bilayers of thin-film magnetic topological insulators
(MTI) with large in-plane magnetization can realize flat bands near 2D Dirac
nodes. Using a simple model for thin films of MTIs, we derive a continuum model
for two such MTIs, twisted by a small angle with respect to each other. When
the magnetization is in-plane, we show that interlayer tunneling terms act as
effective $SU(2)$ vector potentials, which are known to lead to flat bands in
TBG. We show that by changing the in-plane magnetization, it is possible to
tune the twisted bilayer MTI band dispersion to quadratic band touching or to
flat bands, similar to the TBG. If realized, this system can be a highly
tunable platform for strongly correlated phases of two-dimensional Dirac
semimetals.
