Parham likely saw the below three flags fly over Mississippi in 1861.
Source of below is ms.gov, the official website of the State of Mississippi.
In 1810, southernmost Mississippi became part of the Republic of West Florida. Then this banner, known as the Bonnie Blue Flag, flew over Mississippi coastal counties. Before this, the U.S. believed it already had acquired southernmost Mississippi when it bought the Louisiana Purchase from France in 1803. But Spain refused to evacuate the area. So, in 1810, American settlers rebelled against the Spanish and drove them east. The Americans then formed the Republic of West Florida and applied for U.S. statehood. President James Madison responded that West Florida already was in the Louisiana Purchase and ordered officials to take possession. Then, that area was added to the Mississippi Territory. In 1861, this flag resurfaced at the Old Capitol in Jackson, where Mississippi had just passed the Ordinance of Secession. Its lone star, again, symbolized a claim of independence.
Mississippi voted to secede from the Union. For a few weeks, the old Bonnie Blue Flag of 1810 was the new Sovereign Republic of Mississippi informal symbol. But on January 26, the republic adopted a new flag with the Bonnie Blue Flag in its canton and a magnolia tree in its center field. When the Sovereign Republic of Mississippi joined the Confederate States of America, on March 27, the short-lived Magnolia flag was replaced by the Confederacy’s flag.
On March 4, 1861, the first flag of the Confederate States of America was born in Montgomery, Alabama. Concern over the similarity of the Confederate flag to the flag of the United States led to a change in design and the Second National Flag. Difficulty distinguishing the Stars and Bars from the Stars and Stripes from a distance, particularly in battle, was one reason given for the change.