I haven't experimented with cayenne, but certainly have with ginger.
Here's how I'd make my first experimental batch if I wanted to add a
little cayenne spice to our ginger Kombucha. If you want to just make
ginger Kombucha, leave out the cayenne step:
*Brew a standard batch of green/oolong Kombucha.
*Use a garlic press to press in ginger juice (we like to put in some
pulp as well). You can also use a juicer if you have one.
*Add a whole cayenne pepper to steep. I would leave it in for 20
minutes, then test it. Obviously, the more time you steep it, the
hotter it will get. Be careful not to oversteep - it may taste good
for a sip or two but drinking a whole bottle of cayenne "tincture"
sounds like way too much!