I have not been able to find him. The following however may be helpful in your search.
CIVIL WAR—PLANTATION DIARY.
MILBURN, THERESA REBECCA. 1844-1933. Autograph Diary Signed "Miss Theresa R. Milburn," 166 pp recto and verso, 4to, Gold Dust, Louisiana, August 10, 1863-May 13, 1865, in pen and pencil. Disbound, first 2 ff with small open tear at foot with loss to text, some general light browning, occasional wear to edges. Laid in are two ALSs to Theresa's sister Sophie.
WITH: Braided hair bracelet, woven to engraved clasp on one end, and locket on the other containing a ferrotype portrait of Milburn's brother, Elijah Curry Milburn.
This diary gives account of Theresa Rebecca Milburn's life for a span of nearly two years at her family's plantation in Gold Dust, Louisiana. Milburn was nineteen when she began, and she describes the goings-on of her life as a civilian in the South. She details the circumstances of male relatives enlisted in the Confederate Army, family business, and her hopes for Southern independence, as well as accounts of numerous encounters with Confederate and Union soldiers. Milburn's diaries reveal the life of a young woman whose experience of the war was largely second-hand, as she writes, "Oh! When will this unholy war cease? I am sick and tired of hearing of Yankees, War and Negroes."
http://www.bonhams.com/auctions/22464/lot/218/
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Elijah Curry Milburn
Birthdate: circa 1836
Death: (Date and location unknown)
Immediate Family:
Son of Henry B. Milburn and Minerva A Milburn
Husband of Anna Marie Milburn
Father of William Henry Milburn, Sr; Herschel C Milburn; Fenwick Leigh Milburn; J. D. Milburn and Carrie Leigh Milburn
Brother of William Milburn
http://www.geni.com/people/Elijah-Milburn/6000000022040815653
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See also:
Civil War Portraits of Avoyelles
The faces of Avoyelles soldiers and citizens who contributed to the cause
Authored by Randy DeCuir
Portraits include:
Curry Milburn
https://www.createspace.com/4177954
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St Landry's Civil War Faces (150th Anniversary of the Civil War in Louisiana) Paperback – December 24, 2013
by Randy DeCuir (Author)
http://www.amazon.com/Landrys-Civil-Faces-Anniversary-Louisiana/dp/1494792427