Just like I would not let a buddy of mine do any Brettanomyces beer-brewing experiments in my winery, so should you not do Kombucha and wine together in your kitchen (or garage) winery. Brettanomyces is a classic wine “spoilage” yeast responsible for a host of off aromas, often described as “barnyard” and “Band-Aid.” In addition, these yeast, which can happily exist on traditional “non fermentable” sugars like pentoses from barrels and cardboard, are notoriously difficult to get rid of once they gain a foothold. They can start living in your drains, on wooden pallets and even your stock of paper wine labels. Yes, Brettanomyces is often an ambient microbe in the air we breathe, but that’s no reason to go inviting concentrated and healthy stocks of it into your cellar.
That being said, if you have a large property and can be sure you are using separate facilities and equipment for each fermentative endeavor, you will have less of a problem and it might be worth a try. However, just by walking from one building to another you will be cross-pollinating one group with another. One solution would be to see if you could do the Kombucha over at a friend’s house . . . and wash your hands well after hanging out in their kitchen!