The relationship between enhancement flow and structure of core-softened fluids confined inside nanotubes has been studied using nonequilibrium molecular dynamics simulation. The fluid was modeled with different types of attractive and purely repulsive two length scale potentials. Such potentials reproduce in bulk the anomalous behavior observed for liquid water. The dual control volume grand canonical molecular dynamics method was employed to create a pressure gradient between two reservoirs connected by a nanotube. We show how the nanotube radius affects the flow enhancement factor for each one of the interaction potentials. The connection between structural and dynamical properties of the confined fluid is discussed, and we show how attractive and purely repulsive fluids exhibit distinct behaviors. A continuum to subcontinuum flow transition was found for small nanotube radius. The behavior obtained for the core-softened fluids is similar to what was recently observed in all-atom molecular dynamics simulations for classical models of water and also in experimental studies. Our results are explained in the framework of the two length scale potentials.