It appears from census data that parents are Harry Sr. and Pauline. They were listed together in the 1930 census as well, but I didn't locate any marriage record. Maybe you can find some resources for Trenton, Grundy, MO that will lead you further.
Good Luck
U S Census, 1940 Ward 1, St. Louis, St. Louis City, St. Louis City, MO
https://familysearch.org/pal:/MM9.1.1/K74N-HKV
head Harry Phillips M 35 MO Occupation Switchman Rock Island RR
wife Pauline Phillips F 33 MO
son Charles Phillips M 8 MO
son Rodney Phillips M 4 MO
residence in 1935: Trenton, Grundy, MO
US Census, 1930 Trenton, Grundy, MO
https://familysearch.org/pal:/MM9.1.1/XHX1-94B
head Harry Phillips M 25 MO/MO/MO
wife Pauline Phillips F 22 MO/MO/MO
