I don't think DE causes detoxification?
Kombucha causes your body to release stored toxins, and to some degree lemon juice does as well. But not a clay substance, I don't think. Normally you would take a clay (therapeutic-grade calcium bentonite being a good one) along with the detoxifiying agent so the clay will absorb the toxins being released. Because if you detox without taking a clay, then toxins will be released into your system and give you headaches. But if you are taking a clay or DE along with your detoxifying agent (kombucha or whatever) then the clay absorbs the toxins and you don't feel so bad.