 Kuykendall was born in 1878 in Hampshire County, West Virginia, into one of the oldest families in the county, which was of Dutch descent. He was raised on his family's farm, where he engaged in agricultural pursuits. Kuykendall was educated in Hampshire County's rural public schools and subsequently completed his post-secondary education at Hampden – Sydney College and Washington and Lee University. In 1901, he graduated from the Cumberland School of Law, then completed a course in jurisprudence at the University of North Carolina School of Law.
