There are two options for migrating email messages.
First most accounts you can use the self-service migration tool available here: Rackspace Migration Wiz
The second option is if your current email account is setup as POP. POP email is typically stored locally on a computer and removed from the mail server after being downloaded by the client. In many cases, this data cannot be migrated with our migration tool when it does not exist on your source mail server.
If you have a POP account you can set up a second account for your new email address and move the email messages inside your email client to the new account. The exact steps of this process depend on your email client. You should reference their help/knowledge base material for further information.