Not a big expert on Flash, but doesn't he have quite highly developed means to access network services? If all you need to do is provide access for the application to the DB, just raise the DBMS external interfaces of the server (if it is about the client application with a Central database) or local (if it is about local application) and please :) it is even Possible for Flash (Actionscript?) there are a variety of adapters, simplifying and abstracting database and, for example, writing SQL queries is not necessary.
But just think, if you really need access to your database or you need data that is stored, and/or the ability to record them, but with additional logic, for example, advanced authentication, and authorization? Then it is necessary to introduce a three-tier architecture — client application -> app server -> database