I wouldn't use the vinegar, its acidic, ruins aluminum. Try TSP, trisodium phosphate in clean water, very good degreaser, alkaline too. Btw, you don't need distilled water, just 'clean' water. Most engine coolants are either ethelene glycol or propylene glycol based, when they get over heated (burnt) they go acidic and start corrosion. That's the whole reason for the flush, unless its contaminated with oil. In that case you have other issues that a coolant flush wont solve. My opinion anyways.
Why do you think you need to do anything more than a simple drain and refill? The fact that you would consider putting vinegar in your cooling system indicates to me that maybe you should have a professional evaluate a course of action for you.
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