A relative requested that I include additional information to my original post.
Family word of mouth suggests that Sol Burchett is closely related to the Kentucky (and possibly Virgina or North Carolina)Burchett families. Though unconfirmed, he was probably born out of wedlock. He might have been raised by relatives other than his parents, and we believe he had half brothers or sisters in the area. His Native American heritage definitely came from his mothers side of the family. It remains unclear if he inherited the surname Burchett from his mother or from his father.
I hope this helps!Please feel free to contact me with any questions.