  The observation of zero field fractional quantum Hall analogs in twisted
transition metal dichalcogenides (TMDs) asks for a deeper understanding of what
mechanisms lead to topological flat bands in two-dimensional heterostructures,
and what makes TMDs an excellent platform for topologically ordered phases,
surpassing twisted bilayer graphene. To this aim, we explore the chiral limits
of massive Dirac theories applicable to $C_3$-symmetric moir\'e materials, and
show their relevance for both bilayer graphene and TMD homobilayers. In the
latter, the Berry curvature of valence bands leads to relativistic corrections
of the moir\'e potential that promote band flattening, and permit a limit with
exactly flat bands with nonzero Chern number. The relativistic corrections
enter as a \emph{layer-orbit coupling}, analogous to spin-orbit coupling for
relativistic Dirac fermions, which we show is non-negligible on the moir\'e
scale. The Berry curvature of the TMD monolayers therefore plays an essential
role in the flattening of moir\'e Chern bands in these heterostructures.
