Brinnon is a census-designated place in Jefferson County, Washington, United States. The population was 907 at the 2020 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 Parso…Brinnon is a census-designated place in Jefferson County, Washington, United States. The population was 907 at the 2020 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.