In pdf format, the video should be a link to an online video source. When the user clicks on the video, permission is requested to open the online content.

You can use Adobe Acrobat to add flash video to a pdf which will work as an embedded video in the pdf. That is the full program, not the Acrobat reader.

I may be mistaken; my main area of experience is Word, not pdf. I have used pdf format for years, though.