I don't think that's possible. It's not set up as an Echo app and in order to upload music to your Amazon Prime music account, you would need to have the music files, which I don't think iTunes allows you to do.
I believe Jeff is correct. You could connect your echo as a bluetooth speaker to your Itunes device, but that's it.
Actually, you do have access to your music files. They are stored in the iTunes directory. I have not tried uploading them to Amazon yet, but I have uploaded my iTunes library to my Google account. I am sure it works the same for Amazon. Should be no problem.