If you review the references about Venus' and Mercury's magnetic fields somewhere below in the colonising Venus thread, you'll see that Mercury avoids solar wind collision with the surface at a field strength of 10^-4 that of the Earth, while Venus with <10^-5 fails.

So in principle, you need a solar storm that is 10,000 to 100,000 times the normal interplanetary field to acheive this.

Now, I don't know what that answer is, but it sounds like a lot. Reading between the lines, sounds like we still need something 100 times bigger than a "major solar flare". (n.b. the discussion here ignores magnetic diffusivity, which means that it would take months to years for an imposed external field to seep into and affect the core. By that time, the storm would be long past and its brief pulse of magnetic wrenching filtered away to insignificance)

For reference, the residual non-dipolar field during magnetic reversals seems to be at least 10^-2 to 10^-3 of the normal field, so normal solar activity would not penetrate. However, a strong storm probably would. In that case, you would get an aurora over the whole sun-facing side, but you wouldn't see it because it would be daylight. :-(

I don't think the atmosphere would get messed up too much, and the thick atmosphere would continue to protect us flatlanders.

However, RL might need to wear a tin hat and lead jocks to go outdoors from the dome!