  We characterize the long time behaviour of a discrete-in-time approximation
of the volume preserving fractional mean curvature flow. In particular, we
prove that the discrete flow starting from any bounded set of finite fractional
perimeter converges exponentially fast to a single ball. As an intermediate
result we establish a quantitative Alexandrov type estimate in the fractional
setting for normal deformations of a ball. Finally, we provide existence for
flat flows as limit points of the discrete flow when the time discretization
parameter tends to zero.
