Under normal circumstances, and with those roles, this should be a few-clicks-and-you're-done situation...simply navigate to the stream, click on the ellipses, click the settings gear icon, and click on the delete/trash bin icon (all in the top-right corner).
Does anyone else in your organization run into this issue? I would troubleshoot by having another individual with the same configuration/interaction roles- on another machine- try to replicate the error. If that doesn't render the same result, maybe it's a caching issue?