For the flushing pump it is best to use a rotary vane pump instead of a centrifugal pump. The rotary vane pumps have a higher efficiency than centrifugal pumps. In a closed loop system a high pressure centrifugal pump will heat the water considerably. This is much less of a problem with rotary vane pumps.
For flushing in almost all cases flushing from a single side is used. Double sided flushing can be used when the workpiece is really thin to prevent warping of the workpiece caused by single sided water pressure.
For a single flushing nozzle with a 2mm orifice at a working pressure of about 6-8 bar, a typical flowrate is 6 liters/min.
Example of a suitable rotary vane pump: