Whoever said that you could not upload MP3 files to your Flickr account. Digital Inspiration has a interesting tutorial on how to upload Mp3 files to your Flickr Account.
The trick will require you to use command prompt to embed the Mp3 file into the image before uploading it to your Flickr account.
Once you have uploaded the image you can send the links to your friends and family, they will need to rename the file to MP3 before they can listen to it.
You can also use the same trick to copy other document formats inside your images and upload them to Flickr.