After I drain the coolant do I have to flush the system with distilled water before I fill it back up with Honda coolant?
I think "have to" is a little strong. It's recommended. You don't want to use tap water which may have minerals which could leave deposits in the small coolant passages. I bought a gallon of de-mineralized water at the local parts store for this purpose. I think it cost me about $5. I flushed it through twice and let the motor get nice and hot in between. From the look of it when draining it back out. I was glad to have done it.
You don't HAVE to but it's a good idea. Distilled water is cheap and if you run it through let the bike get hot so the thermostat opens and the water runs through the system. To me it's worth dong it.