I don't see your William Douglas Shrout, but various children of Noah Shrout b1806 at Fleming Co, Ky and his wife Nancy A. McClain b1803 at Ky went to Missouri and are buried at Blue Springs Cem, including David D. Shrout b8 Jul 1830, died 1894 at Blue Springs, Jackson Co, Mo married to mary Ann Atchinson.
John Hood Shrout b8 Jul 1830 Bath Co, Ky, died 6 Feb 1912 Blue Springs, married to Janella Richards first, second to Mary Richardson.
Jackson Newton Shrout b8 Jun 1830, died 19 Feb 1911 at Jackson Co, Mo married to Sarah McMillen then to Josephine Clayton.
James McVey Shrout b8 Aug 1843, Bath Co, Ky died 5 Aug 1924 at Blue Springs,married to Eliza Bessie Johnson
your William Douglas probably decended from one of these
They left Bath Co , Ky for Missouri in abt 1865 Larry Phalin