In what year was the US flag officially established?

While no actual evidence exists that Betsy Ross sewed the first US flag in 1776, it was the Second Continental Congress which passed the Flag Resolution on June 14, 1777 establishing the 13-star/13-stripes Flag, symbolizing the 13 Colonies, as the official US Flag. The resolution stated:

"Resolved, that the flag of the United States be thirteen stripes, alternate red and white; that the union be thirteen stars, white in a blue field, representing a new constellation."

In 1795 two stars and two stripes were added for Kentucky and Vermont. However, in 1818 Congress determined that on the Fourth of July following each state's admission a star would be added, but the original 13 colonies would be represented with 13 stripes. Thus, the US Flag has 50 stars representing the 50 States and 13 stripes.

There is evidence that Congressman Francis Hopkinson, from New Jersey, designed the first flag. On May 25, 1780, Hopkinson sent a letter to Congress asking for a "Quarter Cask of the Public Wine" as payment for designing the flag. He was never paid as he was already compensated as a Congressman.

While no flag exists, in 1870, Betsy Ross' grandson, William Canby, made public the story of his grandmother having designed the US flag. Her daughter, Rachel Fletcher, provided an affidavit that stated the Flag Committee had given her mother a "drawing roughly executed" and Ross made some modifications to it. History without evidence is difficult to prove or disprove.