Is it possible to export the private key within the domain key created on SMG?
The domain keys generated on SMG include an RSA key pair: a public key and a private key. SMG uses the private key to create a signature, which is then added to the header and body of each outbound message. The recipient's mail server uses the public key to validate the message. You can retrieve the public key from the Control Center UI by navigating to Administration > Settings > Certificates > Domain Keys, selecting the created domain key, and viewing it. However, the private key cannot be exported.
As a workaround, you can create your own private key and then import it into SMG as a domain key, as detailed in the article "The same DKIM record for multiple control centers."