From here:

On June 14, 1777, the Continental Congress approved the design of a national flag.

Since 1916, when President Woodrow Wilson issued a presidential proclamation establishing a national Flag Day on June 14, Americans have commemorated the adoption of the Stars and Stripes in many ways–displaying the flag in the front of their homes, parades, and other patriotic observances. Prior to 1916, many localities and a few states had been celebrating the day for years. Congressional legislation designating that date as the national Flag Day was signed into law by President Harry Truman in 1949; the legislation also called upon the president to issue a flag day proclamation every year.

Read it all from the Library of Congress.

And check out this interesting webpage from History.com for all kinds of info about Flag Day, including tips on how to properly display a flag. Happy Flag Day!