While you can access both Alarm.com accounts with one login if you are using ADC Multi-System Access, there is still a unique primary login for both accounts.
You should be able to set up your second system’s primary login to set up the Alarm.com Skill with your second Echo.
If you log into the Alarm.com website and navigate to the Profile tab, select “Manage Logins” Hover over the login names and it will tell you which is the primary login associated with the location account you are currently logged into.