If you can't get a free.kindle email address, then you can try adding a book to Kindle using one of the other methods for adding a book to Kindle that we explain here.
Regarding the free.kindle address, it's a bit buried, but we do explain why we do this here https://leanpub.com/user_dashboard/kindle under the "Add a Kindle" link. If you can't find a way to get a free.kindle email address, then we're afraid our system won't work for you, sorry.