There is some fairly tight integration between MySQL and Flash Builder using PHP. Have a look at http://www.flashrealtime.com/flash-builder-4-and-php-data-services/comment-page-27/ or just search for Flash Builder PHP MySQL. Flash Builder will even build PHP classes to model the tables on the database.
Thats a great tutorial I have definately bookmarked it for reference.
But that uses the PHP and Mysql on the developer's local machine. I need
this to be on a web server using a database thats on the web not local
on my computer.
In other words I can build what I need locally, but I need it to work
when its uploaded to the live server too.
Okay. Same answer really. Most hosting providers will provide MySQL database connectivity as a default option (e.g a2 hosting). Then when you deploy your app you are still talking to a database on the localhost (the web server) since your code is there too. You can also write an AIR app that runs on your desktop and talks to the database on the web server using the same PHP stuff but just pointing to the remote I.P address.
For testing I use MAMP (mac) which gives me MySQL, Apache and PHP in one install.
So you are saying that if I just leave the settings as localhost it should work live as long as I have the database structure etc the same on the remote server?
Perhaps I am way over thinking this?