Amazon Cloud Player remains a digital locker which means that users have to upload their own music files.
They get no option to let Amazon scan their existing music libraries and replicate the same online.
Apple offers this as a paid feature on their iTunes/iCloud platform.
Amazon is now said to be in talks with all the major music labels to get the necessary licenses to offer a similar service to their users.
Google Music also has a similar problem. They also were supposed to be in talks but looks like nothing has materialized till now.