Radiator Flushing?

I would just drain the system completely and refill. While the system is empty, a visual inspection of the radiator thru the pressure cap should give you a good feel for what the health of your cooling system in general is. Forget the radiator flush. If you're really concerned, pull the cylinder off and check out the water jackets.

As far as removing the paint.........
There is in fact 'proper' radiator paint. However, unless you suspect that the rads are not working properly because of the paint I would leave them alone. If you chemically strip them it could be a real nightmare to clean all of the paint goop out of the fins...

Hope this helps!
Chris

Blacks droplets in the coolant may be oil, check your waterpump seal.