My problem is writing the code in Flash for this function.

1) How do I write a SELECT statement in Flash AS2 to find the Username in the Database?
2) After the SELECT statement, how do I get it's results in order to determine whether the Username does or not exist and so inform the User accordingly?
Zinc, and other SWF2EXE applications that do the same job, provide ActionScript libraries that expose the functionality of the SWF2EXE tool.

In the example above, I've shown the SWF Studio commands you would need to talk to any database that you have an ADO provider for. in this case it was an Access database but there are ADO providers for every major database out there.

To query a MySQL database using Zinc you'll have to find the Zinc commands that let you access the MySQL database. Then you'll need to find an example that shows you how to perform a query and read the results as well update the database to do what you want.

My answer to clydde showed how to query an Access database and look at the results. This sample example can be made to work with MySQL by changing just the connection string (assuming the database in MySQL was the same as the Access database). That's the beauty of using ADO for your database access, it's pretty much database agnostic.