Try free searches at familysearch.org. From 1900 census it shows father as JF Kendrick. From searching him - you will find marriage as a widower to Susie Steele in 1900 and marriage o Georgia Johnson in 1896 - likely parent of Roy and Katy.
Groom's Name: Joseph F. Kindrick
Groom's Birth Date: 1866
Groom's Birthplace: Tazewell Co. Va.
Groom's Age: 34
Bride's Name: Susie Steele
Bride's Birth Date: 1867
Bride's Birthplace: Tazewell Co. Va.
Bride's Age: 33
Marriage Date: 11 Jan 1900
Marriage Place: Tazewell Co., Virginia
Groom's Father's Name: W. P.
Groom's Mother's Name: M. T.
Bride's Father's Name: I. B.
Bride's Mother's Name: ---
Groom's Race: White
Groom's Marital Status: Widowed
Bride's Race: White
Bride's Marital Status: Single
Indexing Project (Batch) Number: M01337-7
System Origin: Virginia-EASy
Source Film Number: 2048451
Reference Number: Taze. Co. Image 330
Groom's Name: Joseph F. Kendrick
Groom's Birth Date: 1865
Groom's Birthplace: , Tasswell, Virginia
Groom's Age: 31
Bride's Name: Georgia Johnson
Bride's Birth Date: 1870
Bride's Birthplace: , Lawrence, Kentucky
Bride's Age: 26
Marriage Date: 15 Dec 1896
Marriage Place: Lawrence, Kentucky
Indexing Project (Batch) Number: M01236-8
System Origin: Kentucky-EASy
Source Film Number: 839986
Reference Number: v13 171