Flushing is very important but only intended for specific situations. For example, if you use soilless medium and ffeed with total synthetic nutrients(and have heavy eater strains), then it would serve you to flush them around the 3rd week of flower. This is because the synthetic nutrients are often chelated with other inert chemicals. When the plant uses the nutrients, the inert chemicals get left behind and eventually build up to levels that can cause problems. Flushing around the 3rd week of flower cleans out this buildup and allows you to feed until harvest without the worry of toxicity showing up 2-3 weeks before harvest.
Now iff you are in organics, then fflushing is not something you would do as it is more detrimental to the organic substrate in the medium. You would only flush organics if there is something really wrong, such as high calcium buildup from having too much calcium holding material in the soil.
I grow in both soilless and in hydro. I use coco coir as my plant/root holding medium, and I use synthetic nutrients with it. I will flush both of my setups at the end of the 3rd week of flower as a rule because I don't have to worry about damaging an organic substrate in the medium and it cleans out my medium and systems so that I can go all the way to harvest without the worry of any kind of buildup throwing off my pH or binding up nutrients.
You don't necessarily want to flush out all of the nitrogen at any point unless you have a significant problem that can only be corrected by cleaning the medium out. Even through fflower the plants need to have a certain amount of nitrogen or they will yellow off too soon. During fflowering, we all cut way back on the nitrogen and some of us will give only straight water during the last 5-7 days before harvest to allow the plant to use up the last of the nutrients as this seems to help the plants be cleaner going into the dryer and curing. But flushing isn't necessarily needed unless there is a significant buildup that is beginning to cause issues just before harvest.
If you are going to take some clones right before flowering you may flush for a week of so. The reduction in nitrogen helps some strains root a little better and faster. But as a general rule I don't think it's to the plants advantage. Like Hushpuppy mentioned, flushing mid-grow helps avoid a buildup when using synthetic nutes.
Feeding every other watering helps with that as well. Good luck.