There is also another John Storms in that county that I suspect is also a son of John, but I couldn't find him with the family.Here are a few marriages which are all in Johnson County Arkansas and appear to match the children in the family.
L. M. Storms 21 Amanda Poteet 17 1 Jan 1891
G J Storms, 26 Lucinda E Busley, 18 13 Oct 1889
S P Harris, 20 O M Storms, 20 21 Aug 1887
John A. Storms, 25 Josephine Allen, 15 14 Feb 1884
James Shultz, 26 Arizona E Storms, 15 25 Dec 1886
I believe the name of the children's mother is going to be Elizabeth since I can see a couple in that county by the name of John and Elizabeth Storm(s) on the census as early as 1850, but I didn't find a marriage record for them.Anyway, it looks like you job should be easy since they seem to have stayed in the same place for a long time.