Since you know when and where Flora died, have you obtained a copy of her death certificate?It should show the names of her parents.Also, hopefully it would show the state where her father was born; too many Tom Mannings on the census index without something to narrow down the search.
You didn't give first name of Flora's husband, so I went looking at your message history and found it is Ernest Gahmo Conner, son of William Conner and Lara Barnett.This will take it back to family of that William Conner, his father also a William.
1880 census Lincoln, Douglas, MO:
Category: Name;Relationship to head of family; Marital Status; Gender; Race; Age; Birthplace; Occupation; Father's Birthplace; Mother's Birthplace.
Rachel E. CONNERWifeMFemaleW40MOKeeping HouseNCIN
Thomas M. CONNERSonSMaleW20MOWorks On FarmINMO
Mary D. CONNERDauSFemaleW18MOINMO
James F. CONNERSonSMaleW15MOWorks On FarmINMO
John W. CONNERSonSMaleW13MOWorks On FarmINMO
William M. CONNERSonSMaleW11MOWorks On FarmINMO
Sintha J. CONNERDauSFemaleW9MOINMO
Margaret E. CONNERDauSFemaleW7MOINMO
Sarah F. CONNERDauSFemaleW6MOINMO
Samuel J. CONNERSonSMaleW3MOINMO
1870 census Douglas Co, MO:
Conner, William, 38, b IN - land 300/personal 1200
" Rachel E., 29, b MO
" Thomas M., 11, b MO
" Mary D., 9, b MO
1860 census Webster Co, MO, pg 837:
Conner, William, 29, b KY - land none shown/personal 178
" Rachel E., 19, b MO
" Thomas M., 10/12, b MO
Page 836, possibly father and brother of above William?:
Conner, Joseph H., 57, b TN - land 920/personal 555
" Effie, 65, b NC
" Caroline, 18, b MO
" Joseph, 14, b MO
" Effie, 4, b MO
Same page, one family between and that might be a married daughter of Joseph:
Conner, James, 36, b KY - land 800/personal 590
" Paralee J., 30, b TN
" Effie J., 14, b MO
" Joseph, 10, b MO
" William, 8, b MO
" Thomas, 4, b MO
" James, 3 b MO
" Mary, 1/12, b MO
I took real quick look at Webster Co, MO GenWeb page, looks like Joseph H. Conner performed several marriages as Justice of the Peache in 1855/56.I do not have access to online census index for 1850, but I suggest you find someone who does and see if William from the 1860 census is in the household of Joseph in 1850.
I'll post this info on the OK where you gave the Conner info, too.
Happy Hunting (^_^)