You cannot load an uncompiled CSS file into your Flex application at run time. You must compile it into a SWF file before loading it.
Loading style sheets at runtime (Macromedia Flex LiveDocs)

You can’t load pure CSS files with actionscript3.0 during runtime unless the stylesheet is compiled into an SWF, what’s up with that? I can remember that back in the day, with my old mate actionscript2.0 we’d have lots of fun loading real stylesheets during runtime, those were the days!