Mini beet protocol is to get rid of
Gallstones and clear the liver and gallbladder.
Or 1-beet-per-day.
You will have to gauge the symptoms yourself to see how you feel.
For kapha and pitta raw beet should be ok, vata might need beet juice.
Beets are extremely powerful foods so they can sort of trump your dosha.
Beets can not only help clear the biliary system but pretty much the whole body via cleaning the kidneys and helping to clear the whole digestive tract.
The mini flush should be ok to combine with a real flush, I see no reason that they wouldn't be compatible.
Make sure you take magnesium glycinate capsules every day 4x per day to help the entire system. Imo magnesium glycinate might be a good upgrade for the flush;
Epsom Salt seems to aggravate a lot of people. I am not sold that sulfate is such an amazing form to take.
Raw ginger and garlic might aggravate pitta and vata.
I think pickled should be ok. Two schools thought: 1) beets must be raw to work 2) beets in any form will still work.
Note: pickled in vinegar...
Vinegar is a powerful bile stimulant, perhaps moreso than any other food. This could work to your advantage or disadvantage.
If you can tolerate vinegar, and feel like it is helping you, then use a good quality raw apple cider or other fruit vinegar instead of commercial vinegar. Some commercial vinegars use wheat and can trigger celiacs or other gluten sensitive snowflakes (just kidding, I'm sensitive to it to).
Some people do very well with properly made apple cider to both dissolve and expel stones.
For vata a good way to get apples down without aggravation is cooking/baking.
gosh, what's vata pitta and kapha?
http://lmgtfy.com/?q=vata+pitta+kapha
edit: D.C. Jarvis
https://www.amazon.com/Folk-Medicine-Vermont-Doctors-Health/dp/0030274109