There are 1 US Post Offices in Kinney County serving a total of 3,598 residents equating to 3,598 residents per post office. It's estimated that approximately 5,743 packages are handled across the 1 county post offices annually. Kinney County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 3,598. Its county seat is Brackettville. The county was created in 1850 and later organized in 1874. It is named for Henry Lawrence Kinney, an early settler."