Epsom Salts have the same effect on the liver as oil... it stimulates production of bile and stimulates gallbladder to empty itself.
It may not be exactly identical as the flush with oil, cause when you flush with oil, your body may also absorb some of the oil, so the oil may get into the liver and may actually have an effect on the liver that is very different than just Epsom Salts , but if you absolutely do not want oil, you can at least try it without oil.