I just figured this one out. Make sure that if you embed a font, that every
font used by the movie is embedded. Because if flex tries to use a font that
is not embedded, Flex will automatically switch to using system fonts. IT WILL
IGNORE YOUR EMBEDDED FONTS.

In my project, I was embedding 2 non-system fonts. The Rich Text editor by
default uses Verdana to display your text size, font, all the control
components that belong to the Rich Text Editor... And since I didn't embed
Verdana, Flex ignored my embedded fonts, and forced the movie to use Verdana.
After I embedded the system font (Verdana) everything worked as expected.

So this fixed the issue:

@font-face {
src:url("AABIGFICTION.swf");
fontFamily: "AABIGFICTION";
fontName: "AABIGFICTION";

}
@font-face {
src:url("Baskerville_Old_Face.swf");
fontFamily: "Baskerville_Old_Face";
fontName: "Baskerville_Old_Face";

}
@font-face {
src: local(Verdana);
fontFamily: "Verdana";
fontName: "Verdana";
}