There shouldn't be any effect. Solar storms cause low-frequency fluctuations that can induce significant currents in very long conductors (like hundreds to thousands of kilometers). It's a very big deal for large-scale electrical grids and any copper communication, but it doesn't matter for anything that isn't hooked up to such networks.

I had a similar thought, if high energy particles damage/affect DNA could these events contribute in some way to a period of more pronounced speciation?

Just moving from a seashore to foothills of a mountain will have a vastly larger effect.