It would help to know more about your database structure. Does it consist of one table or many tables?
You should really think in terms of exporting from tables rather than from layouts as you could have many layouts that all refer to the same table. Think of layouts as the method you must use to specify the specific "base table" from which to construct your export.
What version of FileMaker is this?
A properly designed Filemaker system should have a an auto-entered serial number that can be used as your unique identifier. If one does not exist it's very easy to add one. Look for a field (often has ID at the end and/or kp or pk at the beginning of the field name) defined to auto-enter a serial number. If you need to add one, just add a new number field and use Replace Field Contents to load this field with a serial number. (You'll need to place the field on a layout and then show all records first.)
You can export data from the current layout or the current layout's table. However, most solutions have at least one layout for every table. If not, a new layout can be very quickly added for this purpose. You are not limited to the fields visible on the layout when setting up your export and you can include fields from related tables as well, though care must be taken to understand the relationships involved in order to get the desired structure in your exported data.