It will depend on the strength of the solar flare, if it is a small one then only the half of the planet that was subject to it will lose all of its electric devices while the other half will remain fine, however if it was an intense one then the whole planet will be affected, however as long as a few nodes survive then that can be enough to bring bitcoin back to life in the case the internet was repaired, however as we have discussed before an event like that will bring us back to the the age before the electricity, the problem is that we do not know how to live like that anymore and we cannot sustain the current population without it, so a massive and widespread famine will happen, and as you can see you will have way more important things to worry about than your bitcoin at that moment.
In the case of a catastrophic solar flare, it's unlikely that a node will survive because how special would that node be for it to survive the solar flare of that scale especially if it's probably just a computer on someone's basement or facility that isn't likely shielded from those solar flares anyway so I don't see how they will be able to survive one. The internet will probably survive if the said solar flare won't hit anything underwater, as far as I know there's already a lot of undersea cable and data storages that's stored in the water but if it will hit it then the internet will definitely go down, this kind of event is something that we can never be really sure until it finally happens.