On average, more than 100,000 American flags fly over the U.S. Capitol a year. Why so many? The Capitol Flag Program, which began in 1937, allows a member of Congress to request a flag be flown over the Capitol on behalf of a constituent. The flag is then given to the constituent.
A 1998 news reports mentions:
Since the program started in 1937, more than 2.4 million flags have been flown over the Capitol and then sold or given away as souvenirs.
The banner year was 1991 when 154,224 flags were flown. Maybe Americans were feeling patriotic because of the Persian Gulf War. Nobody knows for sure.
The biggest single day for flag-flying was July 4, 1976, the U.S. bicentennial.
A 2002 article reports a similar surge in 2002 after the 9/11 attacks:
This year, I'm anticipating we will break the record for the most flags flown in one year. Most years, we fly 100,000 flags. This year we will fly upwards of 150,000."
I can't find any more precise numbers than that. It appears they're not published.