When I needed to clean mine out, I used Prestone's super flush with good results. Had it not worked, I was seriously considering the same stuff I use to clean firearm brass with excellent results.
I mix a couple of tsp . LemiShine and a few drops of Dawn dish soap in a 2l-sized ultrasonic cleaner (or just a bowl of water) for brass casings, and they come out bright, clean, and shiny. The Citric acid in the LemiShine will actually turn the rusty/oxidized (to the point of black) brass somewhere between pink and "brass-colored" again.
I can't see where this combination of chemicals would hurt anything in the radiator or engine, but I wouldn't want to leave it more than a half-hour or so...and I'm not sure about the soap in that context.
Of course, I was also thinking in terms of "this radiator is cashed in--if I can save it, great" which may not be your position...
If I were going to hit a cooling system with the lemi-shine, I'd probably put about a half-cup of lemi-shine in the mix. I'd also pre-mix it instead of pouring the powdered stuff into the radiator directly.
Just a thought. I agree with 69bee in that vinegar would work -- but in my experience with brass-cleaning, the vinegar should be neutralized and the citric acid doesn't need anything more than a flush/wash.