After the end of a Sprint, many times there are some undone items left. How best, as a Scrum Master, can I ensure the Team is able to do all the stories/tasks that were picked by the Team for the Sprint?
Also, what are the best communication channels for sharing the red flags with management and the business about the delay in specific stories or tasks?
You're asking two separate questions and your first question seems to already exist as a different Question, so I'm going to answer your second question.
[W]hat are the best communication channels for sharing the red flags with management and the business about the delay in specific stories or tasks?
A board.
Information radiators are much more efficient than information pulls.
Simply keep your board both:
...and it should give management the information it needs without interrupting the Team's flow.
It is not wise to think management and business will like to pull the information from the board.
If management doesn't want the business to work in an optimally efficient manner, then that's their prerogative. It's not your responsibility to force management to make sound decisions.
What is your responsibility, though, is to make sure they have all the available tools to do so. Give them access to the board, suggest that they use it, and warn them about the detrimental effects of status pulls.
After that, if they ignore you and continue with the status pulls, simply accept that things aren't going to go optimally and it's not your fault.
