According to census records I located, Hiram J. Dungan is brother to James Thomas Dungan, both sons of James R. Dungan and Amanda McDannal.
James and Amanda Dungan, as Duncan, are listed in the census for 1880 > MISSOURI > AUDRAIN > SALT RVR. James is 46, b. KY as are both parents and a farmer. Amanda is 49, b. KY, father in PA, mother in KY. Children are:Nancy age 19, Amanda age 13, Ida age 7, James T. age 16 and Hiram J. age 5, all b. MO.
I have not yet located the parents of the James H. you found in 1910. He is perhaps a cousin but his father is born in a different place than James T. Dungan.
1900 census Montgomery Co, MO:
Dungan, James, h, b Aug 1871, 28, md 3 yrs, b MO, VA, MO
James Thomas Dungan married Mary A. Toalson.
1910 census Montgomery Co, MO:
Dungan, James H., h, 38 M(1) 12 yrs, b MO, KY, MO
" Maggie, w, 40 M(1) 12 yrs, 4 ch, 4 lvg, b MO, MO, VA
" Arlene, d, 11, b MO
" Arthur, s, 11, b MO
" Kenith[sic], s, 8, b MO
" Montie, s, 4, b MO