While there have been 'workarounds' in the past, the answer is ultimately that codecs that support this are limited and unreliable. You'll need to use a <canvas> trick to really pull this off which involves separating your alpha channel into its own video, then using an invisible canvas to process the video based on the alpha channels (reading pixel by pixel to determine what opacity percentage to draw of every single pixel). Some people use a specific color in the video as the channel (for instance if you just needed red text, then use a different background color as the alpha). You then draw that to a visible canvas after calculated. It's very unideal but there's no "best way" to do this currently, outside Flash.
Thank you for the explanation and tips! Really a pity there isn't a good method for achieving this for a multiplatform end result as of today, you could create really good stuff with it!
Is this something Adobe might be working on, the possibility to put html5-convertable videos into Flash, or is it by technical impossibilities this can't be done?
It's the lack of codec support, which Flash has. Flash's F4V codec directly supports alpha channels which is why we got so used to the luxury.
Sometimes in the real world it amazes me. We're all starting over, learning how to do the same exact things we've always wanted, thrusting a bunch of technologies that cumulatively can't hold a candle to what Flash already made so simple. This is very much reinventing the wheel.
Years and years ago with FP11 for mobile was still being developed I tried a bunch of my Flash work on my old Samsung Galaxy S3. Despite using lots of video, large bitmaps, complex tweens and animation, it handled it extremely well. It looked great. Now that devices are about 10x faster or more, it would only be that much better. *sigh*