I did not find him buried at the State Hospital Cemetery, sometimes called the State Home Cemetery. This is the cemetery for the Winfield State Hospital. I could not locate a dc for Delbert L Thomas in Kansas.
I believe this family is listed twice in the 1930 census, once in Kansas, and once in Texas. The 1930 census in Texas list that Delbert, age 3, Dennis and Elizabeth, were all born in Texas, but Margaret was born in Kansas, age 0. The 1930 census in Kansas, list that Margaret, age 0, and Delbert, age 2, were born in Kansas, and parents born in Texas. Maybe they are not the same family?
In 1940, parents are listed in Kansas with son James, age 5 and Margaret, age 10. Delbert is in the State Home in Kansas, at age 11.
Do you know when Dennis and Elizabeth Thomas died, and where they may be buried? That might shed some light on where Delbert might be buried. Do you know Elizabeth`s maiden name? It is possible that the parents buried him in a family plot.