I couldn’t find any substantial information on this. Kombucha is fermented, which doesn’t indicate vitamin K content – natto and sauerkraut have vitamin K, but yogurt (including Greek) does not have vitamin K. The only nutritional breakdown I found was this for citrus kombucha, saying 0 mcg of vitamin K.
My understanding is there are no clinical trials or sound scientific evidence to substantiate the numerous claims – my investigation supports that. That is not to say there are not any benefits from drinking the tea; it simply means there is no evidence that proves the benefits claimed. Eventually that will change, and I look forward to finding out.
As always, if you consistently consume roughly the same amount of kombucha – it’s not an issue, as your dose will already account for it. However if you occasionally binge, I would recommend testing weekly and often. If you’re really keen, keep a food diary and get an INR test the day after having kombucha. This way, you can work at determining if the kombucha is the cause or not. What constitutes a “binge”? I don’t have the data to say, but 2+ cups when you don’t do it regularly is a good place to start.