I just created a few templates for Mailchimp and upon import, I repeatedly received the following error message:
"The archive was empty or otherwise corrupt"
There was no obvious reason for this message, since the archives seemed just fine and I couldn't find anything that would make this error appear. I'm not sure why, but in my testing efforts to solve this I renamed the archive files from "Archive 1.zip" to "Archive1.zip", removing the space in the filename and it finally worked.
Apparently Mailchimp doesn't like spaces in the filenames of ZIP files that you want to import. If you do run into this problem, just remove the space in the filename and it should work as expected.