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Typically DNA testing is done with y chromosome DNA, yDNA, or mitochondrial DNA, mtDNA. The y chromosome is passed from father to son the way a surname is passed down. Since Pocahontas was female she would not pass yDNA to future generations, John Rolfe would. Mitochondrial DNA is passed from a mother to her children. It follows the female line down from mother to daughter; since a male does not provide the egg, he cannot pass on mtDNA. If Thomas Rolfe was the only child of John Rolfe and Pocahontas there would be no mtDNA passed down. In this case there would be no way to prove descent using the above indicated DNA.
However, these two sources are not the only DNA a person has. One's nuclear DNA is inherited half from the mother and half from the father with only the material in the y chromsome being readily traced back through the male line (females, of course, do not have a y chromosome). With each new generation this inheritance gets mixed with a new source of DNA. Half of Thomas Rolfe's DNA came from his father and half from his mother. Each of his children would receive half of their DNA from Thomas Rolfe which in effect would ensure that 1/4 of their DNA had the same values as those of Pocahontas. You can see how this would dilute the number of values by 1/2 for each generation. While this indicates that there should be some measurable DNA values attributable to Pocahontas, it also suggests that there will be only a small percentage of any random sample of tested DNA values that have been inherited from Pocahontas. If you consider that at present we don't know which of these values are passed on from one generation to the next and which are lost for any given person, we could test the same values of 50 people who are indisputably descended from Pocahontas and get 50 different values and not know which value, if any, was the one that Pocahontas had! Well, it's not really quite that bad since each marker tested probably has only a small number of possible values it can take, but you won't know if the value came from Pocahontas or someone else who had the same value by chance. This also brings up the possibility that there may be an undocumented native American in a line who has provided the native American values rather than Pocahontas.
So, considering all of that, there are companies that test large numbers of DNA markers making it likely that typically native American values would show up in the DNA of a test subject. If enough people tested, and it may need to be a hundred or more, some idea of some of Pocahontas' DNA marker values might be gained. Right now the best test for this costs about $400.00, I think, so for only about $40,000.00 you might begin to get an idea of marker values that would suggest descent from Pocahontas, or maybe not.