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Depending on how intense you want to flush...
First you're going to have good drainage holes in the pot so excess water easily passes through. Then just water as usual - but a lot.
Perhaps someone else has exact figures, but I would say probably somewhere between half to equal volume of water to soil.

I suppose purified water is prefered, but I've just done it with regular water to rinse all the nutes out.

The problem here though, is that 2 gallons with small plants will take ages to dry out, like a week or more, which is not a healthy environment for a plant, nor will you be able to administer nutes for that time.

So maybe in your case you don't want to do an extensive flushing, maybe just a good hard watering, just to dilute the soil.

Another idea that might work, which is what I did in the same situation as you, (though in reverse, long story lol) when I flushed small plants and they took forever to dry out due to large pot size, is flush just the area around where the roots presumably are. E.g. start rinsing out and diluting the soil where the roots are, which means the soil will dry quicker and allow more repeated and frequent diluting/flushing till things are looking better.

The cotyledons fall off eventually anyway, are you sure you need to do this? Pics?

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