He is not the son of John Galtney Kennedy of Henderson County, TN.
Sources
↑1870 Census: "1870 United States Federal Census," database with images, Ancestry Sharing Link - Ancestry Record 7163 #7883418 (accessed 23 December 2022), George Kennedy (24), Farm Laborer, in Williamson, Texas. Born in Texas; citing Year 1870, Census Place Williamson, Texas, Roll M593_1609, Page 428B.
↑1880 Census: "1880 United States Federal Census," database with images, Ancestry Sharing Link - Ancestry Record 6742 #7785104 (accessed 23 December 2022), George Kennedy (35), married, Farmer, head of household in Precinct 3, Lampasas, Texas, USA. Born in Texas; citing Year 1880, Census Place Precinct 3, Lampasas, Texas, Roll 1316, Page 312D, Enumeration District 087.
↑1900 Census: "1900 United States Federal Census," database with images, Ancestry Sharing Link - Ancestry Record 7602 #74969744 (accessed 23 December 2022), George Kennedy (54), Farm, head of household in Township 1, Chickasaw Nation, Indian Territory. Born in Texas, USA; citing Year 1900, Census Place Township 1, Chickasaw Nation, Indian Territory, Roll 1849, Page 26, Enumeration District 0161, FHL microfilm 1241849.