It is not possible to directly switch the email address you use to access Flashissue because your account is directly attached to your Gmail address.
However, you can move you mailing lists over to your new account.
Be sure you log into the correct account before signing up.
You can also export your mailing lists and then import them to your new account.
You can also add your old account as a team member to your new account. From there save the templates on the old account as team templates. You should then still have access to the templates you wish to keep. There really isn't a direct way to bulk move over templates.