How can I save a Flash or .swf file in AVI (or another video) format without losing quality?
It's all about the codec (the algorithm that compresses it). If you choose "No Compression" (or "None" in Quicktime) you'll get a full quality video, but very large file size.
If you intend to share it, consider using the MPEG4 container via H.264 or x264 codec. Great quality to compression (although lossy) ratio.
As long as you don't have code in your animation then just hit File->Export->Export Movie, then configure the options.
Here's an article on exporting sound, images and video. Just skip on down to exporting AVI and it explains the process. The codec is in the Video Compression section. When you click Settings for Video Compression, the codec is in the drop-down at the top. There's various kinds but to get lossless quality AVI you'll have to choose Uncompressed / None for full quality. Again, the file will be huge and you'll need to use another program (like Adobe Media Encoder) or Microsoft Windows Media Encoder, etc, depending on what format you intend to compress it ultimately.