No problem in combining the Keto diet with occasional liver flushing.
What is important is that on the day of the liver flush, you avoid consuming any fat foods. That is all.
What you do the other 13 days between flushes, it is up to you, consuming diet composed mainly of healthy protein and healthy fats will only benefit your liver.
If the keto diet is not good for you, your body will tell you. Not all diets fit all people.
An important part of Keto diet is bone broth with bone marrow, usually cooked 24 hours ( bones cut into pieces to allow for bone marrow to melt and dissolve into the soup + water + Sea Salt + juice from one lemon or equal amount of apple cider vinegar ).
Acid from juice help dissolve natural minerals in bones, making the broth stronger.