The Army Corps of Engineers also does a lot of flood management work, and they use a cost/benefit analysis when deciding which projects to approve that takes into account the value of the real estate being protected. And even then, the local community has to put up a large share of the funding. So it definitely ends up favoring richer communities.

99 Percent Invisible did an episode about this recently:

https://99percentinvisible.org/episode/nbft-05-the-little-le...

Would be an interesting relationship to explore. I think you can look at it as both cause and effect. Effect in that flooding destroys wealth and often-flooded areas will not have longstanding infrastructure or buildings - hits to the local real estate that result from flooding can affect non-flooded buildings as well. The cause could be because property and income taxes in low-income regions may be insufficient to fund infrastructure or public works that prevent or mitigate flooding and flood damage.

Extreme example, but I saw a video of a "homeless" family in Japan that lived on a flood plain. They lived there because it was the only free spot.