You don't. You convert your mov file to a mp4 h264 encoded file, and import that into Flash. Then export to swf (in a folder), and you use that swf in your page (do not forget to upload all the other assets as well).
Alternatively, convert to html 5 video files which are also supported by mobile devices.
Learn more here: http://diveintohtml5.info/video.html
ps you can use the Adobe Media Encoder to convert your mov files to h264. Or to html5 video:
How do you open the mp4 h264 encoded file with FLash (now Animate)? It doesn't recognise the file type.
With such expensive and high level software, It is hard to believe that Adobe CS doesn't convert an H.265 (mp4) to .swf so the video plays on a browser. Dreamweaver has a link spot for the .swf file to play the video portion of the video. Without the .swf file in dreamweaver, only the audio plays in the browser. Seriously missing something.