Since your content is stored locally, Flash Player is likely preventing it from playing per normal security settings.
You should add your local Dreamwaver Site folder to Flash Player's list of trusted directories on your computer, then see if it plays properly.
(Dreamweaver adds an exception for itself, which is why it plays within the application.)
To add a trusted directory, open the Settings Manager: http://helpx.adobe.com/support/documentation/en/flashplayer/help/setti ngs_manager04.html
For instructions, and additional information on security of local Flash content, see this article: http://helpx.adobe.com/flash-player/kb/communicate-internet-flash-cont ent.html
