Electrokinetic transport in nano slits is important due to its applications in electrochemical systems. Typically, ion transport and flow can be described by the Nernst-Planck equations coupled with Navier-Stokes equations. However, it is difficult to accurately predict ion distributions and flows in highly concentrated electrolytes such as ionic liquids. By using modified Poisson-Nernst-Planck (PNP) model, the over-screening and oscillation of space charge density and ion concentrations in ionic liquids could be captured. By using the modified PNP equations coupled with Navier-Stokes equations, we studied ion transport and flow inside a nano slit with finite length. The wall is partly charged with two uncharged regions at the two ends. We found that, as the length of the charged region grows longer with those of uncharged regions unchanged, the velocity distribution in the slit gradually becomes similar to the typical plug-like distribution. This indicates that uncharged regions can strongly affects the electroosmosis. Moreover, the occurrence of the vortices in transition regions between charged and uncharged regions has been observed. This is mainly caused by impedance of the fluid in uncharged regions and the distortion of electric fields by surface charges. This study provides insights into ion transport and flow pattern of ionic liquids in charged nano slits.