  We study electron-electron and electron-phonon mediated pairing in the
Holstein extended Hubbard model on the Kagome lattice near the van Hove
fillings, and investigate their combined effects on electron pairing states. We
find that their combination can promote exotic pairings in a crossover region,
where the filling is close to a van Hove singularity. In particular, at the
$p$-type van Hove filling the $E_{1u}$ ($p$-wave) and $B_{2u}$
($f_{y^3-3yx^2}$-wave) pairings become leading, and at the $m$-type van Hove
filling the $E_{1u}$ and $A_{2g}$ ($i$-wave) pairings get promoted. Moreover,
we show that the electron-phonon interaction acquires a significant momentum
dependence, due to the sublattice texture of the Fermi surfaces, which can
promote non $s$-wave pairing. We present a detailed analysis of these pairing
propensities and discuss implications for the vanadium-based kagome
superconductors AV$_3$Sb$_5$.
