The quickest way to answer your question (imho) : a good SQL query using QGIS DB Manager.
You choose Database / Database Manager / Database Manager then Virtual Layers / Qgis Layers and you can then try the following query (you open the SQL window by clicking on the 'wrench' icon) :
SELECT LU.type, sum(st_area(st_intersection(LU.geometry,FLO.geometry)) FROM LU, FLO
GROUP BY LU.type
I called LU the land use table and FLO the flood table.
You get the cumulated areas of land types in your flooded zone. Once executed u can retrieve the result in your QGIS session :
Check the CheckBox "Load as new layer", fill in the fields expected by QGIS and then click on "Load Now !" - The result of your query will appear in the layer manager.