I've never had any problem with just filling rads with warm water and shaking them up \ pouring them out, until the water comes out clean. I've heard of people just connecting them to a tap and letting warm water flow through them for an hour, or making a temporary loop with some vinegar added. I'm not sure what effect vinegar may have on o rings and stuff so I never bothered.
If you want to be thorough and use CLR still, I would recommend rinsing with water first until you get the bulk out and then a single rinse with CLR. No reason to spend a fortune on gallons of CLR if you can get the bulk of the stuff out with plain water first.
I would do the final rinse with CLR or distilled water to get all the minerals out. If you can make it happen, rinse with automotive antifreeze or something like that. Not sure I'd use green, but maybe VW G12 coolant or something like that.
Mayhem's Blitz part 1 is a product specifically designed to clean new PC watercooling radiators. The first time I used it, it was on a radiator that I had "cleaned" previously with a hot water/vinegar mix. I was startled at the amount of crap that came out of it with Blitz.