I have not really worked with gifs and flash together, but it seems to me that your gif is getting compressed by flash and becoming pixelated. Sometimes flash’s default settings do not work very well, what I would do is double click the gif in your library and that will open up the properties window that flash uses for that image and see what you can come up with.
Or, wait for someone else with more knowledge than I (there are many) to have a go with your question.
The reason that it gets pixelated when you zoom in, though, is because Flash simply can’t smooth out images from external sources. When you make an image in Flash, Flash views it as “line line box box fill circle box” or whatever. When you import an image into flash, Flash will view it simply as “image”.
You could probably remake that .gif in Flash. If you did that everything would work fine.
If you have trouble doing that try tracing it. Flash is a great way to trace things; just put the image on a background line and replicate each line one by one on different layers until they fit in perfectly. Then just delete the layer with the original image in it.
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