I don't know about shrubs that will soak up water after flooding but there are large shrubs that will cope with very wet and sodden land. Cornus Alba Siberica and its variants and the Willows will thrive in these conditions. If these sort of shrubs are not suitable then perhaps you might need to look at some hard landscaping with soakaways.

That would be a very bad thing to do. The shrub roots will tightly compact the earth around them and make the ground impervious to water percolation. The hard earth which will be slightly raise by the root ball will create a levee which is exactly what you don’t want. I had a water buildup against the side of one of my previous homes from a privacy hedge line planted by a previous owner. After cutting the hedges down I had to remove the root balls to allow the water to drain away from the house which it then did but the ground was so hard around them I was thinking about renting a jackhammer to help me along with it. Well, my youth and intense anger at this job did the trick.

The best advice I can offer is look to your native plants & shrubs to your particular zone. What works for me, may not work for you. Look at all the swamp grasses, cat tails, reeds & rushes that grow in the Louisiana swamps. They all protect the city from storm surges & hurricanes that come ashore and land erosion. Also Sweet Bay Magnolia is used for flood control, Water Irises, Hydrangeas, willow trees always want to be near water, swamp maple, winterberry, bayberry, etc.

Thank you everybody for your replies.