Brinnon is a census-designated place in Jefferson County, Washington, United States. The population was 797 at the 2010 census. The community is named for Ewell P. Brinnon, who in 1860 took a do…Brinnon is a census-designated place in Jefferson County, Washington, United States. The population was 797 at the 2010 census. The community is named for Ewell P. Brinnon, who in 1860 took a donation land claim at the mouth of the Duckabush River. Its known landmarks include Dosewallips State Park and Black Point Marina. Camp Parsons, founded in 1919 and the oldest Boy Scout camp west of the Mississippi River, sits just outside the north end of the CDP.