Kenney is an unincorporated community in northern Austin County, Texas, United States. According to the Handbook of Texas, the community had a population of 200 in 2000. It is located within the Gre…Kenney is an unincorporated community in northern Austin County, Texas, United States. According to the Handbook of Texas, the community had a population of 200 in 2000. It is located within the Greater Houston metropolitan area.