Thank you for the invitation. It sounds like a most interesting exhibit. However, Dwight Eisenhower was the fourth president to be represented by three different flags. Theododre Roosevelt was the first. Roosevelt inherited two presidential flags from William McKinley: a naval flag which was simply the coat of arms of the United States, in full color, on a blue field (flags flown from ships were made of wool bunting, fringed standards made of silk were used on parade.)
Presidential Flag 1900 Navy Version - Silk Presidential Standard | Flickr - Photo Sharing!
The Army had a scarlet color which consisted of a scarlet red silk field with a blue star bordered in white in the center. The star was surrounded by 45 white stars, plus one larger star in each corner. The coat of arms of the US was on the central blue star.
President Taft Breakfast Plate 1911 | Flickr - Photo Sharing!
Shortly after taking office, Roosevelt was asked which was his proper flag, the red one or the blue one? Because the Navy flag was older, Roosevelt proclaimed that the the Navy flag should be used. In 1902, a third flag was designed for use in peacetime which consisted of the US coat of arms on a blue field, with the exception that the eagle's feathers were white to provide more contrast with the dark blue field of the flag. (the crest over the eagle was altered as well in minor details.) However, the Army decided to keep its scarlet color for ceremonial purposes. If you go to Wikipedia and search for "presidential flags" you will find an article illustrating these and other flags representing the POTUS.
In 1912, President Taft had both the blue and red colors, and again tried to make them consisten. Instead, the Army took their scarlet color and reversed the scarlet and blue so that the field was blue, but the inner star with the coat of arms was scarlet.
Finally, in 1916 Woodrow Wilson got rid of both the earlier navy and army flags/colors and had Byron McCandless design a flag which was the white eagle facing right on a blue field, with a white star in each of the four corners.
In contrast, poor Harry Truman only served under two flags: the Wilson flag and the one with the POTUS seal surrounded by 48 white stars on a blue field.