Literal belief in the flood story

[Esquilax]

If you're asking what 'problem did the flood solve permanently?', then I'd have to think more about it, but for now I'd have to say I don't know of any problem it permanently solved. If your asking what issues were temporarily solved a few come to mind.
1. The world was no longer exceedingly wicked (though wickedness and its potential were not permanently eliminated).

I consider near omnicide far more wicked than anything we humans could have been doing.

2. The bloodline for the messiah was protected and maintained.

Omnicide wasn't required for this.

3. God's wrath was temporarily satisfied.

This isn't a "problem" that needs resolving, it's your god being a psychopath.

4. A prototype for Christ was revealed.

Omnicide wasn't required for this.

True it didn't solve the problem but I'm not convinced the text says it is meant for a solution to the problem rather than a consequence for it. The text says it was because of something God did something. If I said I went to the store to buy milk because I was in need of milk and had none, would you conclude that I bought milk to solve my lack of milk problem? Certainly you wouldn't conclude that I bought milk at the store to permanently solve my 'milk need' issue. You would accept that buying milk was a consequence of having no milk, not necessarily a permanent solution to the problem of not having milk. So why the difference in conclusions?

Because "kill every living thing in the world bar a small number," is not a justified consequence of any action that could possibly happen, ever. It wasn't necessary, and your god's little tantrum doesn't have a valid justification after the fact: "Well, everyone was wicked! Of course he needed to murder them all!" isn't an argument.

We'd have to get more into the character and nature of God to fully explore the reasoning here. Understand, God is Holy (set apart), and God is just. God actions are always consistent with His character and nature. If God is Holy and just and acting in a manner consistent with His character and nature, then at the proper time justice would be brought about. God acts because it is His nature to do so.

That's circular reasoning: who told you god was just? Was it, perhaps, the bible?