  Following Donaldson's oppenness theorem on deforming a conical
K\"ahler-Einstein metric, we prove a parabolic Schauder-type estimate with
respect to conical metrics. As a corollary, we show that the conical
K\"ahler-Ricci Flow exists for short time. The key is to establish the relevant
heat kernel estimates, where we use the Weber's formula on Bessel function of
the second kind and Carslaw's heat kernel representation in \cite{Car}.
