I found two Burlington Plantations in VA. Not much on the one in Orange Co. It is now a wedding venue,
BURLINGTON PLANTATION, VA. 1818: OUR HISTORY
Burlington Plantation is a classic farm style home built circa 1818 eleven miles west of historic Williamsburg, Virginia.
The main house was started by the Edwin and Sara Major family in 1815 and initially completed in 1818. The Major family continued to occupy and improve the main house, doubling its size around 1840. After 1859 the property passed to John Mumford Gregory, a member of the Virginia House of Delegates and Governor of Virginia. The property changed hands five more times over the next 130 years.
https://www.dailyprogress.com/orangenews/opinion/buried-truth-carolyn-howard-french---eclipse-award-recipient/article_2d630988-cc9a-11e8-b17c-cffdeab2f442.html
Carolyn French was born in Washington, D.C. on January 23, 1927. She was the daughter of Dr. William J. Howard and Dorothy Waring Howard. Her ancestral roots run deep in Orange County. Her great-grandfather, John Albert Brown, was born on the Burlington Plantation and her great-grandmother, Winifred Simpson Brown, was born on the Barbour Plantation.
The Other Burlington Plantation, King William, CO,VA
Gwathmey family papers, 1790–1982. ca. 10,000 items. MssG9957cFA2. Microfilm reels C259–261.
The Gwathmey family of Burlington plantation played a prominent role in the history of King William County. Joseph Gwathmey (1758–1824) was the first to own Burlington. His oldest son, John Hill Gwathmey, lived there until his death in 1839, at which time John's brother, William Gwathmey, a physician, moved his family from Wakefield to Burlington. William's son, Joseph Hardin Gwathmey (1846–1918), was an agent for Virginia Fire and Marine Insurance Company and superintendant of schools for King William County. His daughter, Mary Burnley Gwathmey (1883–1974), pursued higher education and obtained degrees in education and design.
In box 1 of the collection are papers pertaining to Joseph Gwathmey's estate. The estate book for 1824–1831 contains his will (slaves referred to generally, not by name) and several references to hirings and purchases. The 1824–1837 book contains a list of about thirty slaves and their values; on page 79 is a summary of the estate division, with children being kept with their mothers. In box 2 are diaries, 1833–1874, kept by Dr. William Gwathmey. Valuable subject notes on these diaries may be found in the cataloging notes in box 1; William made references to significant events but rarely elaborated on them, so details are scarce. Some of these events are hiring day, the hanging of John Brown, the baptism of slaves, Reconstruction, and the mistreatment of slaves.
The story of Sylvia Hill is the focus of a folder in box 52, which contains the papers of Mary Burnley Gwathmey. In the early 1940s Mary Burnley decided to write the story of Sylvia Hill, a former slave who continued to work for the family and maintained close family ties until her death in 1906. The folder contains a typescript of the work, approximately twenty pages. The collection also has other notations of Sylvia in various places: her will is in box 11; in box 7 is a deed of gift for a house and lot for the length of her employment with the Gwathmeys; and in Dr. William Gwathmey's 1857 diary he indicates that she married Dennis Hill on 3 January.
https://www.virginiahistory.org/collections-and-resources/how-we-can-help-your-research/researcher-resources/guides-researchers-2--6