Please follow the below link for moving the BizTalk 360 database from one instance to another instance
For Moving the BizTalk 360 database along with the BizTalk 360 application :- Please proceed the following steps
1. Deactivate the license,If it's an manual deactivation,you can find our link for information.
2. Move the BizTalk 360 database as mentioned in the link.http://assist.biztalk360.com/solution/articles/1000237324-moving-the-biztalk-360-database-to-new-sql-instance
3. Uninstall BizTalk360.
4. Reinstall BizTalk360 (with new Database name example: BizTalk360new) in the new machine where you want to move application
5. Delete the new Database.
6. Rename the Old Database with new Database name.
old DB name: BizTalk360 and
new DB name:BizTalk360new,( Delete the new Database and change the old database name as old =BizTalk360new.)
So that you can use the old Database without loosing any data.
Note: please ensure if BizTalk360 is installed in multi-server, upgrade BizTalk360 Monitoring services in all the machines without fail.