Data is stored in SWX files, that is read natively by Flash Player as "objects".
Can the client request the server to update/modify SWX files, much like a MySQL database? How? SWX-PHP?
You would have to read SWX files on the server side. This would propably be quite hard to do, and not very practical.
You might consider storing your data in a database instead (for instance MySQL) and access it using for instance SWX-PHP services.