Having spent more time on the research and asking other developers I put together a small list of possible alternatives to using SWF assets for animation. Hopefully it will help other developers, who has a similar problem while the SWF animation support is weak.
NOTE: all methods were selected considering three factors important for me: availability on all platforms, performance and file-size of assets. Therefor not all possible methods were included.
Tested on: HTML5, Android, iOS
SWF animation is possible with Haxe/OpenFL, but there are few rules: no tweens - all animations are frame-by-frame. Vector art should be cached as bitmap, saved as bitmap or pre-rendered as bitmap sequence as on some platforms (e.g. neko) vector art is being transformed to raster with ugly bitten edges. Some bugs were reported if representing MovieClip's as graphics or vice versa, but I didn't notice any bugs on HTML5, Flash, iOS, Android releases. Nested animations sometimes might skip frames if looped (didn't see that either, maybe older release of NME/OpenFL did that). I'd say this is a fairly good way to animate content from the concern of file size and platform availability, but it's a headache to edit all the assets to meet requirements of Haxe support. And it's not fun to reuse these assets later, since they're all frame-by-frame animations and it's a mess.
Sprite sheet animations. Primary used for HTML5 targets due to higher rendering performance. This is directly from a openGL standard, so this method should apply for all openGL targets. The idea is to rather have one big file and save time on opening/loading multiple smaller files. The performance is good, works on all tested platforms, but the file size get's quickly out of hand and can be hardly used for animations where object size is changing in size - makes unnecessary large transparent space, rotating the image to best fit the space reduces rendering performance with editing the transformation matrix on run-time.
Frame sequence aka PNG sequence animation. Personal favorite. It works well and fast on all platforms, it's possible to pre-render the the animation (just like any other method above), transform to BitmapData array, stream-load etc. It does take a lot of disk space for the animations, but can be softened by loading the assets before using them (HTML5, SWF) and it doesn't really matter for mobile devices - as even 1-2GB apps are ok for the market. Large advantage that I found for myself is that this type of asset can be used for any other developing standard (C++, Java, cocos2d) and saved as Sprite sheet if needed (e.g. cocos2d, like HTML5 prefers Sprite sheets over anything else as written in the official book COCOS2DX by Roger Engelbert).
With this flexibility, good performance is tolerable file size I prefer this method over any other method listed above.Bone animation - PNG array + property list. Another approach is having separate images of an animated object and every image matrix data for every frame. That way with minimum disk space use it's possible to make thousands of animations. The downsides are: it's harder (not impossible) to have nested animations for more complex animations, constant matrix transformations limit number of active animations on the display list (horrible method for HTML5, other platforms held on well) and little reusability of assets. Usually it's the same good old SWF assets that were exported to this type, so it makes sense to edit the FLA rather then the bone animation itself.
Surely I've missed some great points, there are many ways to animate graphics and some might work for you better than others so feel free to leave comments and criticize, but I still hope this topic was helpful.