When it is believed by one of the parties in a conversation or brainstorming that everyone has reached a consensus on a topic and therefore they all can move to the next phase. The hope is that everyone will say it eventually to indicate their personal commitment ('sew me') to the decisions that have been agreed to ('a flag'). It was purportedly first used in 1776 by George Washington to Betsy Ross to get that whole flag project going. Popularized again in 2011 by musical improv team Mansical with their performance 'Flag' at a New York improv festival (youtube - phrase is used at 2:12). It is most effective when used with the 'Betsy Ross' lead-in as shown in the example, but the generic version is more typically heard in business settings.
Betsy Ross!! Sew me a flag!!!!
by Crazytown Industries February 1, 2014