There are a few things that you can do to reduce the file size of an exported SWF from ID.
1. Use master pages. If you place an item at the same location on every page, just use ID master pages. As long as you don't override them in ID, they will be treated 1 image upon export.
2. Use the JPG pass through filter. If you place a JPG at 100% in InDesign and do nothing to it, ID will export it as-is and not re-compress it. Since PS does a better job of making smaller & better quality JPG's, this would save you file size.
3. Use 72 DPI JPGs for all of the images in your layout and place them at 100% (see above tip).
4. If you are using video, stream the video (link to a URL) rather than embeded
5. Simplify your layout. If you can use simple color backgrounds instead of bitmap images and go easy on the effects (like drop shadows).
6. Reduce your documents dimensions. Since your SWF file is going to be online, you don't need to have it be the size of a printed page. If you create a document that is smaller (600×300) your overall size will be smaller.
Good luck and please share the link to your online magazine, I would love to see it.