Presidential flag from about 1902, which was used until 1916.  In 1902, the question of having two presidential flags (one from the Navy and one from the Army) came up, but instead of choosing one, this third flag was designed instead.  It was supposed to be used for peace display only, with the other two being used in times of war, but all three were used until they were all replaced by a new flag designed during President Wilson's term in 1916.
The design was essentially the same as the Navy's presidential flag, which was the Great Seal on a blue flag, except that the eagle was changed to be pure white (like their original 1882 presidential flag) and the crest was changed to not show the clouds, but instead just a sunburst of rays in a complete circle around the stars.  
More information here.

The dimensions of the flag were 10.2 feet hoist by 16 feet fly.  While the original naval order specified to use the same size as the Admiral's flag, the 1899 Flags of Maritime Nations published by the Navy gives separate dimensions for the President's flag of 10.2 x 16 (as mentioned on the Sea Flags site).  The Admiral's flag per the same publication was 10.2 x 14.4 feet.  These were the "size no. 1" dimensions; the "size no. 6" dimensions for both flags was 3.6 x 5.13 feet.  However, one book[1] says the dimensions were 10.6 x 14 feet.
Alteration of File:US Presidential Flag Navy 1899.svg, patterned and colored per File:1902USPresidentsFlagBook.jpg and File:Making president's flag 1914.jpg. SVG Great Seal  taken from File:US-OfficeOfManagementAndBudget-Seal.svg, a U.S. Government work, with the crest altered.
U.S. Government