There is a Flood Zone Code that displays on the Flood tab on the Full and Flyer displays in Matrix that shows the flood zone that the parcel is in. There are many instances, however, where a single parcel is located within multiple flood zones:
If any part of the parcel is within a flood zone, that is the zone with which the parcel is associated. In the above example, the parcel is actually within two different zone (X and AE). Since part of the parcel is located in the AE zone, that is what displays in the Flood Zone Code field.
The MLS has nothing to do with flood zone determinations- those are done by FEMA.