The current way the extension is trying to use for its CSS does not load the CSS, because it is passed through the parser and thus filled with tags, at least in MediaWiki 1.22. I'd very much either change the hook it uses for that or pass the sanitized CSS into the style attribute of the output tag, but I figure it'd be better to ask beforehand, as this is a nontrivial change.
Topic on Extension talk:DynBox/Flow
Apparently this extension is currently unmaintained. It also has a freaky XXS alert warning. I guess it would be cool to overhaul this extension completely. You should probably take over maintaining it. In this case just remove the unmaintained template. Cheers