Use organic apple juice to dissolve the salts instead of water. Much better!

You can use magnesium citrate this will relax the ducts too. Or if you want to buy supplements you can go to Julia Chang's website http://www.sensiblehealth.com they help too but they need a little bit longer time for preparatoin than apple juice.
Since you did The Clark Flush I wonder if you stopped eating and drinking after 2 pm.
It is important to drink enough water after 2 pm (it is not mentioned in The Clark Flush ), a lot of people got dehydrated and got nauseous when they did not drink enough water.

This does happen from time-to-time. The most common reason is because you have insufficient bile or pancreatic juice to deal with the quantity of olive oil and lemon juice. You can reduce the amount of olive oil and lemon juice by a third or half for the next flush and then build up again. You have to judge how much you can tolerate.

Epson salts are a type of laxative that can cause dehydration. On the day of the flush make sure that you eat simple meals and drink PLENTY of water so that your urine is running full and clear before you take the flush mixture. But it probably wasn't the Epson salts that made you vomit it was the quantity of the flush mixture.

If really don't want to take the Epson salts then miss them out and take a senna or Oxypowder early the following morning to clear out the intestines.