well, I have absolutely no idea what I'm looking for in your code, but one thing I did find was this:
PHP Code:
$update = "update customers set FName='$fname'; LName='$lname'; where customerid='$cid'"; 
semi-colons in MySQL, like in PHP, are terminators. this lets both MySQL and PHP know that this is the "end" of a command. you're ending your SQL query early. if that query executes, every first name would be set to $fname, and PHP doesn't let you run multiple queries with one call to mysql_query(). however, the rest of the queries would produce errors, and I don't know if MySQL would outright ignore them because PHP might only send the first query, or if MySQL will see your entire query and just fail altogether or at least send back a failure message after successfully querying the first query (thinking about it now, that would be an interesting thing to test). now, hopefully you can make sense of that.

either way, the whole issue before was you weren't even connecting to the database server before and you never fixed it (or you apparently never understood what I was talking about when I kept linking you to your own files on your server that were not connecting to your database). if all of your scripts work fine on your personal webserver, then it stands to reason that you might just be doing something wrong on a live server. post links to every single full URL that your Flash file interacts with so that I, or you, can make sure they are actually connecting to the database this time.