  We theoretically study magnetic and topological properties of
antiferromagnetic kagome spin systems in the presence of both in- and
out-of-plane Dzyaloshinskii-Moriya interactions. In materials such as the iron
jarosites, the in-plane interactions stabilize a canted noncollinear "umbrella"
magnetic configuration with finite scalar spin chirality. We derive expressions
for the canting angle, and use the resulting order as a starting point for a
spin-wave analysis. We find topological magnon bands, characterized by non-zero
Chern numbers. We calculate the magnon thermal Hall conductivity, and propose
the iron jarosites as a promising candidate system for observing the magnon
thermal Hall effect in a noncollinear spin configuration. We also show that the
thermal conductivity can be tuned by varying an applied magnetic field, or the
in-plane Dzyaloshinskii-Moriya strength. In contrast with previous studies of
topological magnon bands, the effect is found to be large even in the limit of
small canting.
