Where do brown dwarfs get deuterium from?

The deuterium burned by brown dwarfs is mostly a remnant of the big bang. Big bang nucleosynthesis primarily created hydrogen-1 and helium-4. It also created small amounts of deuterium, tritium, and helium-3, and very small amounts beryllium-7. The tritium and beryllium-7 soon decayed to helium-3 and lithium-7.

Most of the deuterium did come from the big bang. However some of it is produced as a by product. For example

$$p^+ + gamma to n^0 + e^+ +nu $$

This induced reverse beta decay could create neutrons that can accelerate into other protons and create deuterium nuclei. This produces energy of roughly 2.2 Mev.

$$p^+ + n^0 to d + 2.2 mev $$

This is also a reaction which could create a very small amount of deuterium. On top of this some decay products could result in deuterium.

This heats up the brown dwarf maybe helping to create more deuterium creating reactions.