How to convert mov to swf

Because the video is buried inside a full SWF file you won't be able to convert it -- it's much like if you had a Mac app that happens to play a built-in video: you're effectively trying to convert the app to a video, two very different kinds of things.

Instead you'll need to extract the video. You can use a task-specific extrator, and since you asked for a free way to do it, I suggest the Flaex app. There are a couple of other paid extractors for the Mac including Flash Decompiler and SWF Decompiler. I don't have first-hand experience with any of the extractors so I can't specifically recommend one.

The other possible not-free way to extract the video is by opening the swf file with the full Adobe Flash Pro, or have someone do it for you. Note that Adobe provides a fully-functional 30-day trial, so at least in the short-term it's a free option as well.

Gif Ninja is a great site for converting videos to gifs. I've used it several times and the gif always comes out great.