This is where the answer lies: http://forums.adobe.com/message/2558650#2558650
It is a nuisance doing it this way, but it was the ONLY method that worked for me.
- Firstly, close Flash.
- Move all fonts from /Library/Fonts & ~/Library/Fonts to a folder on your desktop.
- Start up Flash again, try opening the file which uses the missing fonts. (You should get the Font Replacement dialog now), click Cancel.
- Quit Flash.
- Move the .ttf/.otf files of the missing fonts (missing in Flash) back to /Library/Fonts, but only them, not the rest.
- Start Flash up again with the .fla in question, your fonts should all be found now and render.
- Quit Flash, move the rest of the font files back to /Library/Fonts (did not test it with User fonts i.e. ~/Library/Fonts, I suppose it would be just same copying them back to ~/Library/Fonts)
- Open Flash again and all missing fonts should now be visible in Flash.
This is the ONLY method that worked for me!