As far as I know, you cannot create SVG files in Flash.
Flash Pro CC 2014 (v22.214.171.124) is now available for download via the Creative Cloud App and Adobe website.
We have added SVG Export feature to Flash Pro with this new release. You will now be able to export out vector content from the selected frame as an SVG image that can be opened directly in a Browser and even imported in Adobe Illustrator.
SVG Export option can be accessed via the Publish Settings as well as via File Menu > Export > Export Image option.
Along with this, we have added several new features with this release. Complete list is available at these links:
Would it be possible for you guys to add a "Minify SVG file" option? Would be nice to speed things up a bit when serving SVGs via the web.
Also - similar to PNG exports - could SVG include a "minimum image area" option?