The day does actually have a relatively long and storied history. On June 14, 1777, the Second Continental Congress formally adapted the Stars and Stripes as the official flag of the United States. Incidentally, on the same day in 1775, the Army was "formally" formed.
The day was never really publicly referenced until 1861, in an encyclopedia about Kansas by George Morris. That being said, the day continued on in relative obscurity until 1916, when President Woodrow Wilson issued a formal proclamation declaring it Flag Day. Congress followed suit in August of 1949 (insert joke about Congress working slowly here).
The day is not a "formal" federal holiday that requires any sort of government closures. Typically, during Flag Day and Flag Week (which is the same time), citizens are urged via proclamation to fly the flag and celebrate everything that it represents.
So - enjoy your Flag Day!
Article any source
