That's backwards. Red dwarfs have extremely powerful flares relative to their luminosity. So much so that it's unlikely that life would survive on the surface of an orbiting planet. (Though life would probably survive underwater.)

https://en.wikipedia.org/wiki/Habitability_of_red_dwarf_syst...

https://en.wikipedia.org/wiki/Flare_star

That's not quite true. These planets are very close to the star and can receive large doses of the little bit of harmful radiation that the star puts out. Additionally, these planets put out a lot of infrared, but not a lot of higher energy photons, and life-as-we-know-it needs those higher energy photons. That infrared is also absorbed by water in any atmospheres or oceans that are present, leaving even less for life. Finally, these types of stars tend to have rather variable output in their spectrums, which may make it difficult for life to adapt.

But the danger of both of those things surely decreases with the square of the distance to the star?

More radiation = more mutations = healthier/faster evolution!

Life is more than capable of evolving mechanisms to increase or decrease it's mutation rate. On Earth Eurkaryotic cells with large genomes have developed nuclei to reduce their mutation rate and bacteria are more of a mixed bag with some even deliberately uping their mutation rate above what would be cause by radiation, etc. So in the long run eukaryotic life would just have to waste more resources on mechanisms to resist the effects of the radiation.

That doesn't follow, at all. If we're talking about Earth-like life, then any such life would need protection from radiation to be able to live long enough to reproduce. If such protection wasn't provided by the planet's atmosphere, then life there wouldn't move out of the water. In any case, the mutation rate would need to be extremely low, as it is with Earth life.

Then the surface of stars ought to have more life than planets.