I am a descendant of this line of Dukes. Thamar/Tamar Taylor's origins are unknown to me. I do not even know how "Taylor" was assigned as her last name. However, I do know that Tamar/Thamar is not a Native American name. It is the name of a river that divides Cornwall from Devon in England. The name appears in a number of unrelated lines in the 1600's and early 1700's in Virginia, perhaps serving as an indicator of ancestry from this region of England.
The relationship to James Duke and Mary Byrd is unproven as far as I know, though members of this family married into prominent families. For example, Tamar Duke, daughter of William Duke and Thamar Taylor, married William Wortham of the prominent Henrico Worthams. This may be irrelevant. However, Nancy Wortham, daughter of William Wortham and Tamar Duke, married William Marshall and had a daughter, Mary "Polly" Green Marshall, who married Spotswood Burwell, grandson of Governor Alexander Spotswood. A connection to the Dukes of James City County and the Byrds of Charles City County is possible -- but still unproven.