I'm using this .gif of Spidey running. Loops go round and around so try to have an animation which is seamless. Since the camera angle changes in this animation the flow isn't abrupted.

This is an example of an animation that isn't seamless since you clearly see when it starts over. This does not mean you can't use it; you never know what animations and music would make a great loop together. But in general you should aim for seamless animations.

Let's start with the music. You should look for songs that fit the animation and vice versa. An upbeat song for a hectic animation or a cute song for a cute animation. Complete opposites might work as well. Experiment!
Using the whole song usually makes the file too big. Cut out a part of the song that loops instead. If you have a song where the chorus is repeated you can easily take one half of it and turn it into a seamless loop since that's how it sounded to begin with.
Begin by dragging the file into Audacity. Highlight the part of the song you want to use and click CTRL+T to remove everything else.

Now begins the trimming. Drag the part all the way to the left to make sure there isn't any empty silence before the song starts. Be careful when cutting around a drum beat since any gap in the rythm will be very noticeable.

To make sure you've got a seamless loop copy what you have and paste it right afterwards. Listen to it and if there are no noticeable gaps where the second part start you're good to go. Press CTRL+Z to remove the part you pasted and export your file out of Audacity.

Open up a new document in Flash and drag your music into the space in the middle. This will make the music appear in the first key frame of layer 1.

Insert as many frames as the music is long. Make sure the frames end just where the song does. Otherwise the looping will be messed up and your song might star playing over itself.

Now to add the animation. Click on Insert new symbol.

Drag the animation into the middle. This will create Symbol 1 down in the library. A symbol is an image or animation that works on its own. In this case meaning that it will loop forever.

Go back to the scene window and create a new layer. Drag Symbol 1 into the middle and the first keyframe of the new layer. Make sure this layer has is just as long as the first layer with the music. Meaning they both have the equal amount of frames.
Open the Align window in case it isn't already up. Click the circled buttons to put the symbol in the middle.

Almost done. The document is still bigger than the animation though. Click on Properties on any of the bitmap files to see what dimensions the animation has. Remember the pixel numbers.

Go into Modify -> Document. Write in the pixel numbers you just checked into the dimension boxes and click OK.

Click the align buttons again and you're done!
You can now watch your loop either by Control -> Test Movie or by pressing Ctrl+Shift+Enter.

To export your loop as a .swf file go File -> Export -> Export movie. Save the file somewhere and this setting window will pop up. Worse sound quality = smaller file. I usually go with these settings. Don't forget to unclick the convert stereo to mono button.

The size of your loop depends on how long the music and animations are and what quality they are in. Shorter with worse quality = smaller file. Try not to go above 2-3 MB in size since sites where you can upload your loops usually have a size limit somewhere around that area.
Another way to make your file smaller is to open the properties on the animation bitmaps and change the file from png to jpeg. Not necessary but small files are always nice.

Open up your loop in a web browser to see how it will look like once you've uploaded it to the interbutts.

Here's how it turned out. Not great by any means but sufficient for this guide.
http://www.spchan.org/res/fr/631.swf

I've posted other loops I've made in this thread. Please excuse the moon runes.
http://www.spchan.org/fr/reply/288.html

Here's another great loop for reference.
http://www.pown.it/2256

Thanks for reading! If there's anything you think should be changed or added, please do tell.

Pretty in-depth; I don't see anything that will really confuse people who are new to this. Just to expand on a couple things, I'm not trying to upstage you or anything:
>>267
An easier way is to align the gif to the top left corner, go the Documents Properties, and just hit the Contents tab. No need to remember pixel dimensions.
>>272
Please at least do 64 kbps. That's already ear rape; I couldn't imagine going any lower.