One thing the article does not mention is the reason for pre-flushing is to ensure the sample is coming from water in distribution, not water that's been sitting in the lead pipes you have in your home or your connection to the city (which is very common in older cities). While Flint performed pre-flushing, they also made sure to test around the lead sites, it's not clear that is what is happening in these 33 cities.
So, if the testers flush when collecting samples, perform the same flush before drinking tap water, that way you know you are drinking water at the levels measured. The most common objection I hear to this suggestion is "What a waste!" However, when you consider that water may not be safe to drink, you're not actually wasting drinking water. If you really are concerned about that water, you can save the water for plants and/or cleaning purposes. Watering your lawn is huge waste of water, running some water to clean pipes is not.
What people should be worried about are endocrine disrupting compounds (EDCs), e.g. from birth control pills and hormones used in factory farming. To my knowledge, no city currently has the ability to test for or filter out EDCs. If the lead tests are coming back clean after flushing, that's great because it's easy to fix: just flush your lines before drinking. EDCs, not so much.
Source: I know many who work for the water department, including chemists at the testing labs at one of the 33 cities listed in the article.