The short answer is that the flag you refer to was (in general terms) devised by Congress's Marine Committee, the main purpose of national flags at that time being simply to identify ships at sea. Great story though it is, dear old Betsy had nothing to do with it and it's probably up there with the story of Washington and the cherry tree.
In 1775, a Congressional committee (Benjamin Franklin, Benjamin Harrison, and Thomas Lynch) consulted Washington on a design for a Continental flag, which resulted in the Royal Navy-style red ensign with six horizontal white strips (often referred to as the Grand Union Flag of the United Colonies, or occasionally the Continental Union) that was flown at Boston. The DoI made British symbology unacceptable, so another committee (Washington, Robert Morris and George Ross) was established in June 1776 to find an emblem acceptable to all 13 Colonies. However, the Marine Committee beat them to it, and Congress passed the Flag Resolution on 14 June 1777. This specified that the flag be a field with 13 horizontal red and white stripes, and a canton containing thirteen white stars on a blue field. As so often with momentous pieces of legislation, the wording was ambiguous - until the mid-19th century, the flag could have more white stripes than red, and stars with six, seven or even eight points (in fact, all previous versions of the flag remain legal, as none were ever abolished as new versions were authorised). Examples of the Maritime flag actually flown include a mix of red white and blue stripes, so even those details that were officially agreed were often ignored.
In September 1779, Washington was being asked to suggest a variation that might be used by the Continental Army, and as the equivalent of the British King's Colour (why they didn't use his HQ flag I don't know). Dark blue was agreed for the field, and appropriate cloth - along with facing-coloured cloth for the "regimental colour" - was issued to the regiments as part of the 1779 Clothing Regulations. Unfortunately, no "national emblem" was agreed for the blue flag before the war ended (there are suggestions the eagle was considered, which of course was later adopted by the US Army). As well as debunking the Betsy Ross story, historians have also discounted the claims that the Maritime flag was flown at Bennington, Stanwix, or Mud Island - in fact, all three appear to have been variations on the Grand Union, but with red, white and blue stripes, and no small Union in the canton.