Where do kombucha SCOBYs get nitrogen?
Short answer:

Nitrogen fixation (i.e, atmospheric nitrogen)

Longer answer:

Nitrogen fixation is the process by which atmospheric nitrogen is converted to forms usable by further biochemical reactions. Some bacteria are capable of nitrogen fixation (and some plants have symbiotic relationships with nitrogen-fixing bacteria); all the others rely on those species directly or indirectly to provide nitrogen.

The microorganisms involve in brewing kombucha tea are actually a collection of different species of bacteria and yeast. The bacteria that are found in kombucha tea include Acetobacter nitrogenifigens and Gluconacetobacter kombuchae, both of which are capable of nitrogen-fixation (and there may be others).

Molasses is also often used as the sugar source for kombucha, and molasses includes some nitrogen-containing compounds.

See the following review for more information:

Jayabalan, R., Malbaša, R. V., Lončar, E. S., Vitas, J. S., &amp; Sathishkumar, M. (2014). A review on kombucha tea—microbiology, composition, fermentation, beneficial effects, toxicity, and tea fungus. Comprehensive Reviews in Food Science and Food Safety, 13(4), 538-550.