Don't flush the new compressor!!!

Flushing is pretty simple, albiet messy. Assuming you have an air compressor.

You can cut down on the mess inside the car by drilling out your old expansion valve, then reinstalling it. That allows you to flush the evaporator from under the hood. Then install the new valve when you are finished flushing.

You could install your new compressor on the engine and just not hook it up, so you can at least drive the car.