When your nutrients are already IN the soil (stuck to cation and anion exchange sites), flushing doesn't do much at all. Yes, you will leach out some of the more soil-mobile compounds like nitrate, but overall, you aren't doing much at all... In healthy soil, the plant is in control of it's nutrient supply and uptake, not the grower. When the plant needs nutrition, it releases H+ and/or OH- ions into the soil solution from it's root tips. These ions released by the roots then "bump" the appropriate nutrient ion off of it's cation or anion exchange site so that it can be taken up by the plant.
This is how plants grow in nature. When you bombard the soil with conventional fertilizer, the salts will eventually build up as water evaporates leaving the salt residue behind. In this situation, flushing can be helpful. In organic gardening, these salt residues never form in the first place.
You will find that with organics, the plant will fade to "fall colors" as it nears peak maturity. This isn't because the soil is "depleted", it's because the plant does not need as much nutrition so it is releasing fewer H+ and OH- ions.