Johnny’s nine times great-grandmother, Nicketti Opechancanough, was of Powhatan Native American ancestry, making Johnny of 1/2048 Powhatan Native American descent.
The claim about Nicketti Opechancanough does not have the same level of scholarly backing. Apparently there is no evidence that such a person existed.
The family trees - all unsourced, and full of fantasies - around Opechancanough Powhatan and the nonexistent Nicketti are a big, old, racist mess.
In addition to evidence quoted by Epiphany, see also NAFPS forum member jeaniesgenealogy's blog:
http://www.jeaniesgenealogy.com/2011/11/im-related-to-princess.html [Princess Nicketti Powhatan]