A review of records at the Burnet County Clerk's Office, Burnet, Texas revealed that John Barton King fathered the following:
Henry Thomas King, born 10/30/1893
Maggie King, born 9/20/1889
Ethel King, born 12/5/1887
Lewis Armstrong King, born 10/21/1891

I wasn't able to identify any additional information. Hope this helps.