  Recent studies have attracted intense attention on the quasi-2D kagome
superconductors $ A\text{V}_3\text{Sb}_5 $ ($ A = $ K, Rb, and Cs) where the
unexpected chiral flux phase (CFP) associates with the spontaneous
time-reversal symmetry breaking in charge density wave (CDW) states. Here,
commencing from the 2-by-2 CDW phases, we bridge the gap between topological
superconductivity (TSC) and time-reversal asymmetric CFP in kagome systems.
Several chiral TSC states featuring distinct Chern numbers emerge for an s-wave
or a d-wave superconducting pairing symmetry. Importantly, these CFP-based TSC
phases possess unique gapless edge modes with mixed chiralities (i.e., both
positive and negative chiralities), but with the net chiralities consistent
with the Bogoliubov-de Gennes Chern numbers. We further study the transport
properties of a two-terminal junction, using Chern insulator or normal metal
leads via atomic Green's function method with Landauer-B\"uttiker formalism. In
both cases, the normal electron tunneling and the crossed Andreev reflection
oscillate as the chemical potential changes, but together contribute to plateau
transmissions (1 and 3/2, respectively). These behaviors can be regarded as the
signature of a topological superconductor hosting edge states with mixed
chiralities.
