I think the issue relates to the fact that you have nested double quotes inside single quotes.
My method of solving this problem is to keep experimenting until it works. In your case, I can't experiment because I don't have MS Outlook. So we will have to wait for someone with Outlook or with more skill at quotes in Shell.
Here is the solution Peter recommended that works:
osascript -e 'tell application "Microsoft Outlook"' -e 'set newMessage to make new outgoing message with properties {subject:"'"$KMVAR_List"'"}' -e 'make new recipient at newMessage with properties {email address:{name:"DSTUrgentRecords", address:"DSTUrgentRecords@google.com"}}' -e 'open newMessage' -e 'end tell'