I personally find nothing wrong with the flush kits you get from Wal-Mart for the DIYer. It gets all the old coolant out and allows you replace it with fresh coolant.

Some will flush it with tap water and then follow with distilled or purified (reverse osmosis'd water) just to make sure none of the tap water minerals remain.

If you get coolant that meets the manufacturer's recommendation/specs then there shouldn't be any compatibility issues.