A common practice is to place the CSS files under <src><assets><styles> directory in your project.
Then, in your MXML file you use them :<mx:Style source="/assets/styles/common.css"/>
When ready to publish to online server, you do as "Export release build" from your project menu.
This will generate all you need files in the "bin-release" directory in your project environment.
You should upload all this content ( from the bin-release directory) to your server.