At the moment, there is no support for this process in FluentMigrator. You could add a timestamp to the filename and then check the size of the file. If it is very small, less than 200 bytes then throw it away. If it is larger than 200 bytes then the schema has changed so rename the file to DBScript.sql and replace the previous version.
I would recommend submitting this as a feature request for FluentMigrator here.