YES. you can migrate an existing environment to a new environment. First you need to update the license key. To get the new license key, write to us at email@example.com with the new environment details.
You can take a backup of BizTalk360 database and then migrate it to the new SQL server. All you have to do is to uninstall BizTalk360 from the old server and Install BizTalk360 Web and monitoring service components on the new server. Monitoring service should be installed where BizTalk server is installed. While installing BizTalk360, simply point the database to the new database location and uncheck installation of database component in the last page of the installer.