The flag with the streamers is in the Oval Office since JFK:

FILM FOOTAGE:

[link to historyinpieces.com (secure)]

JFK is Presented with the U.S. Army Flag in the Oval Office

In a brief Oval Office ceremony, Chief of Staff of the Army General Earle Wheeler and Secretary of the Army Cyrus Vance present JFK with the U.S. Army Flag with battle streamers. The flag is then placed behind the President’s desk.