In my game Hudriks I also used flash to design levels and even make some animations.
There is no any tool to do this, so you need to develop it yourself with requirements for your game.
First of all, it depends on your game and what exactly you need to design in flash - just putting images, defining their parameters (bonus values), ground path, etc.
After that it is important to define structure of your flash file - how you store different levels (in symbols or scenes), what layers for each level you have (boundaries, objects, obstacles, etc).
If you need to have some extra information for you objects in flash, most probably, you will need to develop custom panel in flash to setup all parameters. I used setPersistentData for storing information for flash objects.
After that you need to develop script that goes through all objects in your symbols and extracts basic information, like transformation, and your custom data. I faced some problems with getting correct transformation values, especially for rotation. Had to do extra heuristics.
For animations I just used motion tween data. In my animation framework did simple implementation supporting basic parameters (transformation and alpha) and only linear curves. Fortunately, in Flash CS4 there is function copyMotion that gives you XML for the animation. You just need to parse it or convert to your own format.