When I try to authenticate using my account name in JIRA or my account name in Google neither works.
You need to use your OnDemand password, not your Google password. This is the password you would have been prompted to create when you logged into Atlassian OnDemand for the first time. See http://confluence.atlassian.com/display/AOD/Changing+Your+Password+in+Atlassian+OnDemand
This is similar to this question.
There are technical reasons as to why we cannot use your Google credentials to provide authentication for RSS feeds.
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