  We consider the flat flow solution, obtained via discrete minimizing movement
scheme, to the volume preserving mean curvature flow starting from
C^{1,1}-regular set. We prove the consistency principle which states that (any)
such flat flow agrees with the classical solution as long as the latter exists.
In particular, the flat flow is unique and smooth up to the first singular
time. We obtain the result by proving the full regularity for the discrete time
approximation of the flat flow such that the regularity estimates are stable
with respect to the time discretization. Our method can also be applied in the
case of the mean curvature flow and thus it provides an alternative proof, not
relying on comparison principle, for the consistency between the flat flow
solution and the classical solution for C^{1,1}-regular initial sets.
