We use Milton as a flushing agent, but we also use sterilising tablets. Once the water container has been filled we just pop one in to ensure nothing nasty starts growing inside! We also use Domestos to clean out the waste water container. A good way to keep it smelling better.
Milton will work well, but the best way to get it working is to leave it in the system for about 30 min .It is a bit like taking a Paracetamol tablet they need time to work . As i work in the water industry this is a practice we use with water treatment. But a very good flush after is the only way to get rid of any taste problems. As long as you use FOOD QUALITY grade piping you should not get any more problems