<p>I know that you can apply CSS in order to style objects in Flex using the StyleManager:<br>
<a href="http://livedocs.adobe.com/flex/3/html/help.html?content=styles_07.html" rel="nofollow noreferrer">http://livedocs.adobe.com/flex/3/html/help.html?content=styles_07.html</a>  </p>

<p>You can also load <strong>compiled</strong> CSS files (SWFs) dynamically:<br>
<a href="http://livedocs.adobe.com/flex/3/html/help.html?content=styles_10.html" rel="nofollow noreferrer">http://livedocs.adobe.com/flex/3/html/help.html?content=styles_10.html</a>  </p>

<p>However, I'm dynamically creating my CSS files using a web GUI and a server-side script.
If the CSS is changed, then the script would also need to compile the CSS into an SWF (which is not a viable option).  Is there any way around this?</p>

The application of CSS in Flex is handled on the server side at compilation and not on the client side at run time.
I would see two options then for you (I'm not sure how practical either are):
Use a server side script to compile your CSS as a SWF then load them dynamically.
Parse a CSS Style sheet and use the setStyle functions in flex to apply the styles. An similar example to this approach is the
Flex Style Explorer
where you can check out the
source
.
Good luck.