You definitely want to flush the system. The inks don't mix well. The basic workflow is, Discharge the ES3 inks, flush the system with Mimaki cleaning solution multiple times (I usually do 3 rounds), discharge the solution so the lines are empty, change the dampers, then fill with SS21.
If you are using white ink I would manually flush those lines after the main flush to make sure it did the trick. White clogs a lot easier and sometimes won't allow the flush to run it's course. Manually pulling some solution through will tell you if it's flowing or not.
Keep in mind that there is a possibility the head doesn't make it through the process 100%. You may lose some nozzles. The odds of that happening are much less likely if you are switching to the same color set. So if you are CMYK x 2 ES3 now and you are switching to CMYK x 2 SS21, it will go much smoother.
You do need to change a few parameters to tell the machine the ink set has changed. I'll need to know your model to tell you the right ones.
Edit: Also just to address one of your first questions, while the inks are incompatible, they both use the same cleaning solution so there is no ES3 flush and then SS21 flush. Just one flushing solution type.
