  Studying the (long-term) behavior of the K\"ahler-Ricci flow on mildly
singular varieties, one is naturally lead to study weak solutions of degenerate
parabolic complex Monge-Amp\'ere equations.
  The purpose of this article, the second of a series on this subject, is to
develop a viscosity theory for degenerate complex Monge-Amp\'ere flows on
compact K\"ahler manifolds. Our general theory allows in particular to define
and study the (normalized) K\"ahler-Ricci flow on varieties with canonical
singularities, generalizing results of Song and Tian.
