Brexit — a group of angry people winning a fight — easily inspires other groups of angry people to start a similar fight, empowered with the idea that they may win.
That alone can trigger chain reactions.
A nuclear explosion is not caused by one atom splitting, but by the impact of the first atom that splits causing multiple other atoms near it to split, and they in turn causing multiple atoms to split. The exponential increase in atoms splitting, and their combined energy is the bomb. That is how World War One started and, ironically how World War Two ended.
An example of how Brexit could lead to a nuclear war could be this: