The liver is not like the bladder. The liver is a solid organ highly vasculated, as opposed to a sac such as the bladder. Therefore one can not expect a given fluid to "flush" the liver.
If the dog has an auto-immune reaction then the problem resides in the immune system of which the liver is not part of. Assuming the liver is not one of the organs undergoing an auto-immune attack, then continued proper diet is all that is required to maintain a healthy liver.
It is reasonable to question the Vet about any side affects of any prescribed drugs per the liver.