this is a problem with the flash player in the webkit browser used by Dreamweaver Live view.
You say that you created a page and added a flash swf file to it, did you then try to view the page in Live View? are you able to view flash files in live view?
see this thread:
http://forums.adobe.com/message/21173
near the end, on user reports downloading the flash version for the Fire Fox browser was able to get flash working for them.