The liver flushes involving the olive oil, lemon juice and magnesium sulfate do not flush out gallstones.  The so called "stones" are an insoluble complex formed from a reaction between the sterols found in the olive oil and cholesterol from food or bile salts in the intestines.  This is why these "stones" float instead of sinking like real gallstones.

It is actually impossible to pass most real gallstones since they tend to much larger than the bile ducts, even when dilated with the magnesium sulfate.  It would be like trying to fit a golf ball through the eye of a needle.   The reason people feel better after this "flush" is because the olive oil helps to stimulate the gallbladder so the bile is not stagnant.  And bile stagnation is a common contributor to gallstone formation.

If people really have gallstones then it is best to dissolve them rather than try to pass them.  Trying to pass them can cause stones to lodge in the bile ducts, which requires emergency surgery.   Most gallstones form as a result of more cholesterol than the bile can dissolve, so the excess cholesterol precipitates out leading to stone formation.  Women are more prone to gallstone formation due to their hormones.  Estrogen stimulates the release of cholesterol in to the gallbladder, while progesterone is a smooth muscle relaxant which increases stagnation of bile increasing stone formation.

Bile itself is a fat emulsifier, and it is the high lecithin content (about 80% lecithin) that gives bile its emulsification properties.  Therefore increasing bile helps to prevent and dissolve gallstones.  Bile formation can be improved by getting plenty of fiber in the diet.

Bitters also help.  As bitter tasting herbs hit the bitter receptors of the tongue the vagus nerve is stimulated.  This in turn kicks up stomach acidity, bile secretion, and pancreatic enzyme release.  This is why these are often sold under the name digestive bitters.  They also stimulate the liver to flush, so it is very important to drink plenty of water throughout the day when using bitters.  This flushing of the liver will also help with hormone regulation as the liver breaks down excess hormones including estrogen and progesterone.

Lecithin granules will also help by providing a building block for the bile.  Make sure to use the granules, not the softgels or liquids, which are highly diluted with soy oil.  The granules provide more lecithin because they are deoiled concentrating the lecithin.   Finally, it is helpful to ingest SMALL amounts of good oils, like olive oil, with each meal to facilitate gallbladder contractions to prevent stagnation of the bile.