  We investigates the electronic structure and superconducting gaps in the
charge density wave (CDW) states of vanadium-based Kagome superconductors
AV$_3$Sb$_5$, focusing on the concurrent presence of CDW and superconducting
orders. Two predominant CDW configurations are explored: the trihexagonal (TrH)
and star-of-David (SoD) patterns, involving charge bond order (CBO) and chiral
flux phase (CFP), corresponding to real and imaginary bond orders. In the
isotropic $s$-wave superconducting state, the presence of CBO alone maintains
an isotropic superconducting gap, whereas the introduction of CFP induces
anisotropy in the gap, manifesting time-reversal symmetry breaking due to the
CFP. Our analysis extends to the topological properties of these states,
revealing a marked topological phase transition in the TrH configuration from a
trivial to a non-trivial state with increasing CFP intensity. This transition
suggests that the introduction of CFP could catalyze the emergence of
topological superconductivity, potentially leading to the presence of Majorana
excitations. The results contribute significantly to understanding the complex
interplay between various CDW patterns and superconductivity in Kagome
superconductors. They provide a theoretical framework for the diverse
experimental observations of energy gaps and open new avenues for research into
topological superconductivity and its potential applications. This study
underscores the necessity for further experimental and theoretical exploration
to unveil novel interwinded quantum states and functionalities in these
intriguing materials.
