There are some interesting studies which record how the biliary system varies over the 24 hrs of a day. These are called circadian cycles. The gallbladder fills overnight and reaches its maximum volume at 9:00 AM after which the volume reduces to reach its minimal volume between 6:00 PM and 12:00 PM. It doesn't have a fixed volume throughout the day and the maximum volume is about twice that of the minimal.
During the liver-flush process you are utilising the properties of the Epsom Salts to caused the gallbladder to contract slightly and then fill rapidly. The amount of contraction is quite variable between individuals but the rapid fill replenishes to gallbladder with fresh liver bile towards its maximum volume.
If you flush in the morning you will have a lower proportion of fresh liver bile in the gallbladder than you would in the evening around 20% compared to 50% gallbladder volume.