The attached screenshot, shows two flood zones (AE-6 & AE-7). The numeral in the flood zone identifier represents the flood elevation level. Also shown are the building footprints.
Using spatial join with the match Option set to "Completely within" easily associated all these buildings with the proper flood elevation,
However, when buildings straddle the flood zone boundary line (see selected footprints in the attached graphic), I haven't figured-out how to get the spatial join to identify the proper flood elevation; in this case "7" feet as opposed to "6" feet. (When a flood zone boundary line touches a building to any degree, the entire building is considered in the higher regulated zone.)