I got a comment on this, I didn't really give enough detail on exactly how I went from a bottle of Tea Chi to having a gelatinous disk of microbes. Essentially, I applied the same principles to get it that you can to harvest yeast from a commercial beer, start small and go bigger as the microbes can handle it. If you go too big too fast the microbes will take a long time to grown and ferment and might get overrun by the local microbes who might not make such a tasty beverage.
I let the whole bottle of Kombucha warm up to room temperature, I then poured it into a sanitized mason jar. I generally don't sanitize now but I wanted to give the microbes a head start because they might be weak after being refrigerated for a couple of weeks. To them I added about a cup of cooled unfermented Kombucha (just cooled tea with .75 oz of white sugar dissolved in it). Every few weeks I would add some more of this sweetened tea moving up to larger vessels when needed until the Kombucha “mushroom” had grown quite large. I dumped out this first batch because it had gotten very sour because of how long the culture had been fermenting without a large replacement or liquid.
When it gets big enough you can just start bottling 90% of the liquid before adding the fresh nutrient solution.