The chemistry behind the flushing formula is quite simple, they contain agents which can make complexes with divalent cations (like calcium and magnesium) and hold them in solution under conditions where they would otherwise not be soluble. EDTA (ethylenediaminetetraacetic acid) is probably the most common of these chemicals, although anybody wanting a similar effect organically could use fulvic acids to achieve a similar kind of effect.
Natural soil solutions will contain chemicals with very similar metal complexing properties (e.g. fulvic and humic acids), so adding these kinds of chemicals isn't introducing any kind of conditions that the plants aren't used to. The same substances are used to provide available forms of various metals such as calcium, magnesium, and iron to plants in a variety of fertilisers, e.g. in sequestered iron.
Personally I don't use a flushing agent, but at least I now understand how they work. They can only really improve the removal of divalent and trivalent cations, so presumably won't really help with removing excesses of nitrate, phosphate, or potassium. On the other hand the addition of heavy metals to soils through repeated applications of inorganic fertilisers is well documented, so there is arguably a better case for using these products if you don't grow organically. I tend to find that un-flushed weed tends to have a slightly metallic taste to it, which isn't present in properly finished weed, so perhaps the focus on removing the calcium and magnesium works. If you plan on reusing your soil you could potentially be stripping all kinds of goodies out of it though.
for example you flush for 1 week. So you win 2 weeks in witch you can still feed and get extra yield.
