  We study the near-the-interface behavior of a compact convex scalar curvature
flow with a flat side. Under suitable initial conditions on the flat side, we
show that the interface propagates with a finite and non-degenerate speed until
the flat side vanishes. Then we get optimal derivative estimates of the
pressure-like function, optimal decay estimates of curvatures near the
interface, and an Aronson-B\'enilan-type curvature lower bound, from which we
obtain the H\"older regularity of the ratio of the curvature to the optimal
decay rate up to the free boundary. In the end, we obtain the short-time and
all-time existence of the solution, smooth up to the interface.
