Paternal relationship is confirmed through Y-chromosome DNA testing. Kenneth Johnson FTDNA kit #202680, and his second cousin, FTDNA kit #177420, match at a Genetic Distance of 2 on 67 markers thereby confirming their direct paternal lines back to their MRCA Håkan August Johnson, the great grandfather of each. FTDNA indicates that the probability the two share a common ancestor within the last 3 generations is 31.83%.
It may be possible to confirm family relationships by comparing test results with David or other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree:
Family Tree DNA Y-DNA Test 67 markers, haplogroup I-M253, FTDNA kit #177420