If you are referring to the olive oil, lemon juice flushes I don't believe in them one bit.
If you want to cleanse the liver safely, while supporting it then I recommend getting some schisandra berry powder. Then I recommend placing 1/2 teaspoon of the powder on your tongue, 3 times daily, and suck on the power for a minute or two before swallowing it. It will go through various flavor changes, which is why it is called the 5 flavor fruit. The bitter aspect will stimulate the bitter receptors on the tongue, which in turn stimulates the vagus nerve. This will cause the liver to flush.
Schisandra berry is also very supportive to the liver, kidneys, and adrenals.
Remember to drink plenty of water throughout the day.