How do I replace a flash movie on a website with a quicktime movie? I don't even know where to begin.
EDIT: In the light of the new information you have posted about your question, I think SuperUser would be a better place for this question, rather than StackOverflow. That being said, on to the answer:
Although fenomas did a great job explaining video conversion to this particular format in a nutshell, this is by no means a topic that can be fully explained in a post, and since there are literally dozens of ways of converting, I will only explain what I did:
Using Adobe Media Encoder I have converted your FLV file to an uncompressed AVI file for further processing (because QT Pro can not open FLV files directly). Although AME has the option of converting directly to MOV, I usually find that it does not provide enough options for the advanced user, thus exporting unnecessarily large files (for .mov videos, at least). Note that an uncompressed video file, regardless of the format will usually be extremely large, this video in particular was over 1.3 GB in its uncompressed form.
I have then opened the exported AVI file with QuickTime Pro, and I have used the Export option to encode it to QT video. I used the h264 codec for encoding the video, with a multi-pass encode and a limit of 1000 kbps for the bitrate to keep the file-size down. Please note however that this is not a "recipe" - these settings must be adjusted depending on the video that's being encoded and it usually depends on the video size. This particular video might be further compressed to an even smaller file-size -- it's all about finding the right combination of file-size and quality. For the audio I have used AAC at a sample rate of 44.1 KHz and a bitrate of 96kbps, which is more than plenty when there is only a voice-over/narration and not actual music.
The video that I have encoded can be found here: http://www.megaupload.com/?d=A3DIBFKC
After you have downloaded the zip file (~26 MB) containing the encoded video, unzip it and upload it to your server, in the same folder as the file it's going to be embedded in (if you do not want to modify the embedding code below). Once the file is uploaded, replace the piece of code that you have posted as a comment to fenomas' answer with the following code:
<object CLASSID="clsid:02BF25D5-8C17-4B23-BC80-D3488ABDDC6B" width="320" height="240" CODEBASE="http://www.apple.com/qtactivex/qtplugin.cab">
<param name="src" value="debbie.mov">
<param name="autoplay" value="false">
<param name="controller" value="true">
<param name="type" value="video/quicktime">
<embed src="debbie.mov" width="320" height="240" autoplay="false" controller="true" type="video/quicktime" pluginspage="http://www.apple.com/quicktime/download/" />
</object>
If everything was done correctly, you should now have an embedded .mov file in your website :)
Hope this helps.
Assuming that your question is how to convert the file formats, please describe your source. Do you only have an SWF file? Or do you have an SWF video player which is playing a video in a separate format (like FLV, F4V, MP4, etc.)?
If your video is in a separate file (FLV, etc), then most any application that converts video formats should do the trick. If you have both a video file (FLV..) plus a SWF file, the SWF probably just contains a player (i.e. play/pause buttons, etc.), and you can probably ignore it and just convert the video. (Also note that for some formats, like MP4, depending on the codec the video may already playable in Quicktime! If you have a separate video file try dragging it into QT to check if it plays before worrying about converting.)
If you have only a SWF, however, then not all apps will convert for you. In general, SWFs can be interactive, and they don't have any particular "length", so some applications will convert a SWF into other formats, but in actuality they're playing the SWF and capturing the output and encoding it into a new video. (And note that this will not work well if the SWF has any interactivity - like buttons that need to be clicked, etc.)