Population is an estimate, as it stands, so I'm assuming you are looking for a 'best-guess' type of workflow that will give the best results for the littlest amount of time spent.
ArcGIS's Tabulate Intersection tool may be of interest to you. You can input two polygons (flood zone and population block groups, for example) and tabulate what percentage of that group falls within a flood zone.
You may also want to try a select by location on the amount of buildings that fall within the flood zones, if you have access to that data. If you have access to your county/locality's population and housing data or land use, you may be able to make even more accurate assumptions using the buildings layer or by tabulating intersections--industrial land use, for example, will not likely have any population associated with it, where residential will--You could clip out residential land use from the block groups and see where that falls within the flood zones.