  Graphene multilayers with flat moir\'e minibands can exhibit the quantized
anomalous Hall effect due to the combined influence of spontaneous valley
polarization and topologically non-trival valley-projected bands. The sign of
the Hall effect in these Chern insulators can be reversed either by applying an
external magnetic field, or by driving a transport current through the system.
We propose a current-driven mechanism whereby reversal occurs along lines in
the (current $I$, magnetic-field $B$) control parameter space with slope $dI/dB
= (e/h)\, M A_{M} \, (1-\gamma^2)/\gamma$, where $M$ is the magnetization,
$A_M$ is the moir\'e unit cell area, and $\gamma <1$ is the ratio of the
chemical potential difference between valleys along a domain wall to the
electrical bias $eV$.
