FileLocator Network stores the search data in the user's application data folder, e.g. On Vista this is:
C:\Users\SomeUser\AppData\Roaming\Mythicsoft\FileLocatorNetwork
The single file 'flr.sdf' is a SQL Server Compact file and can be copied and used for backup/restore purposes.
To change the location of this file modify the dbconfig.xml file in the install folder, e.g.
C:\Program Files\Mythicsoft\FileLocator Network\dbconfig.xml