What privileges does the SQL Azure Migration Wizard need to copy a SQL Azure database?
From 
Copying Databases in SQL Azure

Permissions

In order to copy a database in SQL Azure, your login requires the following permissions:

On both servers: The login must have the same login name and password on both SQL Azure servers. 

On the destination server: The login must be a member of the server-level dbmanager role. Note: the server-level principal of your SQL Azure server is not a member of the dbmanager role, but automatically has the same permissions. For more information about managing logins in SQL Azure, see Managing Databases and Logins in SQL Azure.

On the source server: The login must be the DBO of the source database. Only the login that created the source database, the DBO, can copy that database to another database on the same server or on a different server.