  We show that a realisation of spectral flow as a coordinate transformation
for asymptotically four-dimensional solutions can be extended to the
non-supersymmetric case. We apply this transformation to smooth geometries
describing microstates of the D1-D5-KK monopole system in type IIB supergravity
compactified on a six-torus, and obtain solutions with an additional momentum
charge. We study the supersymmetric and near-core limits of this construction.
