You can perform a silent installation of BizTalk360 using the following command -

Start msiexec.exe -i "Installation file path" /qn /Lv* "R:\Install Logs\install2.log" IIS_WEBSITENAME=1 WEBSITE_DESCRIPTION="Default Web Site" WEBSITE_PORT=80 WEBSITE_IP=* WEB_APP_POOL_IDENTITY_NAME="your username" WEB_APP_POOL_IDENTITY_PWD="yourpassword" WEB_APP_POOL_IDENTITY_CONFPWD="yourpassword" CONNECTION_STRING="Server=(local);Database=BizTalk360;Integrated Security=True;" SERVICE_LOGIN_TYPE=2 LicenseAccepted=1 SQL_SERVER_NAME=Server_Name DB_NAME=BizTalk360/Custom_Name

Please make sure you make the appropriate changes in the command and redirect the logs to the log file. You also need to remember that if you use the silent installation command, it would take some time to react.