I am not sure about the exact mechanism or chemistry of how the liver produces bile, but one thing I am pretty sure is that the liver needs nutrients(raw materials) for bile production. As we live in this modern world, due to improper life style and/or eating habits, our body's reserve nutrients gets depleted faster than we can replenish them. When the liver is not receiving what it needs, it will perform poorly and eventually lead to the formation of Gallstones due to liver stagnation and low bile production. I think most of the time, people with trouble on Liver Flushing is due to insufficient bile that is needed in order to push the garbage out, and when the more stones are formed, the situation just gets worst as time goes by.
In Chinese Medicinal practice, the liver is consider a Yang organ, which means it has a hot and with fire characteristics, so the liver has a strong affinity for cooling herb, and the cooling herb can then provide nutrients for nourishing the liver. (No wonder the western doctors call the liver a chemical factory of the human body. It has to work hard continuously through out our life time).
Anyway, there are many kinds of liver tonic, and most of them should have a cooling or neutral property that can supply back the proper nutrients (Chinese call it "yin and blood") which the liver needs for its function, so the liver can have a chance to recover.
The common herbs are: Goji berry, Rehmannia Radix (Su-Di, cooked and pre-prepared already), Polygonum Multiflorum (Heh-So-Wu), White Peony Root. There are more, but I think most people will have a hard time getting it unless they have a Chinatown nearby which sells herb, so I don't think is practical to mention here. But if you really want, I can research first because I only know the Chinese name but not the botanical name.
It's a good idea to take some liver tonic herb as you do the liver flushing. It is just like cars need gasoline to run, but when the gas almost goes out, making the car go up the hill will just make the gasoline use up faster. In this case, doing a Liver Flush with liver deficiency is like having the car go up the hill with insufficient fuel.
Of course, there are restrictions. I like to mention about that since liver tonics are cool and damp in nature, which means caution should be taken for people with weak pancreas and digestion power before taking those herbs, these herbs tend to attract candidas and weaken the pancreas even further because of the herbs' natural "cool and dampness" characteristics. (In TCM, weak pancrea can also be caused by a dysfunction liver too, fire attacks earth, the pancreas is consider the earth element). So take these herb with small amount, if diarrhea, excessive gas, or loose stool ocurrs, either take them not so often, or take pancrea-support herbs during meals that can strength the digestion power, such as the common ginger, spicy kimchi, or hot spices like curry or pepper.
As the liver function gradually improve by flushing and taking tonic herbs, then you can also gradually increase the amount of the tonic herb to rebuild the liver.