This is sort of on the more realistic side of worldbuilding, but maybe somewhat exaggerated for the sake of a setting. What's the fastest atmospheric pressure drop in weather records? This question is kind of more asking how quickly a flash flood could happen, especially maybe a decade in a future. Of course, heavy rainfall contributes to that, but a storm surge caused by wind and pressure is what I'm interested in.
Global warming ==> big hurricane with storm surge ==> landfall into a funnel-shaped bay ==> huge wave/flood up the bay!
FYI, the sharpest barometric pressure drops are (I'm pretty sure) inside tornados -- but those are too short-lived and move too erratically to cause the sort of flooding you're seeking.
Instead, consider the phenomena knowns as Tidal Bores:
https://en.wikipedia.org/wiki/Tidal_bore which tells us that the largest one on earth is:
Qiantang River, China, which has the world's largest bore, up to 9 meters (30 ft) high, traveling at up to 40 kilometers (25 mi) per hour
So this gives you both a ballpark flood height and a speed.
It's apparently popular for extreme surfing (video; I couldn't make this up): https://www.youtube.com/watch?v=XvO5Ckd7mlU
Now, imagine the storm surge from a big (possibly global warming enchanced) hurricane, making landfall into a bay/river prone to tidal bores. Head for high ground.
My creek flooded in 10 minutes. One moment I was standing on the bank, the next I was watching my dumpster float away, after that, I was carrying my baby brother and my precious belongings up the hill because we could not get out of the valley. So flash floods can happen fast.