Copper doesn't rust mate, as it isn't made of iron.
The flux used was water insoluble a while ago, so vinegar was required. The fluxes have been water soluble for some time now (couple of years maybe?), so hot water/dilute vinegar will now do fine. Boiling water from the kettle followed by deionised is probably fine if you're in a soft water area. Hard water would tend to coat the inside of the radiator with limescale, which would suck.
I'm in a very hard water area, so get bottles of deionised water, microwave them and use that. Fill with hot water, give it a shake, leave it for a while, shake again, and empty. Or some variant of this. Don't be too surprised if it comes out clear the first time though, I've read in a few places that xspc appear to flux their radiators before sale.