It is not proved that John Burkett married to Sophronas Reynolds was the son of Jackson Burkett.
http://familytreemaker.genealogy.com/users/r/u/s/Jerry-B-Rush/WEBSITE-0001/UHP-0433.html
John Burkett was born Sep 1854 in Arkansas, and died date unknown. He married Sofroney Summers on 1875. (I believe that this marriage is incorrect)
More About John Burkett and Sofroney Summers:
Marriage: 1875
Children of John Burkett and Sofroney Summers are:
1. +Marion F. Burkett, b. Jan 1879, Chester, Arkansas, d. 20 Mar 1955, Fort Smith, Arkansas.
2. +William T. (Willie) Burkett, b. Apr 1881, Chester, Arkansas, d. 05 Apr 1955.
3. +James Frank Burkett, b. Jul 1883, Chester, Arkansas, d. 11 Jun 1961.
4. +Jacob (Jake) Burkett, b. Jun 1885, Arkansas, d. 11 Jun 1961, Arkansas.
5. +George Burkett, b. Jan 1887, d. date unknown.
6. Saproney Burkett, b. Dec 1890, d. 1903, "Burned to death...got too close to fire while washing"..
7. Thurlow Burkett, b. Jul 1892, Chester, Arkansas, d. 05 Aug 1960, Riverside, CA.
8. Jermiah E. Burkett, b. 09 Mar 1895, Chester, Arkansas, d. 29 Jun 1968, Prarie Grove Cemetary, Prarie Grove,.
9. Eva (Lockey) Burkett, b. Dec 1896, Chester, Arkansas, d. date unknown.
10. +Clementine (Clemie) Burkett, b. 11 Feb 1888, Mountainburg, Arkansas, d. 05 Aug 1960, Ft. Smith, Ark. St. Edwards Hospital, Fort Smith, Arkansas.
11. +Ance Jewel Burkett, b. 09 Mar 1895, Arkansas, d. 29 Jun 1968, Prarie Grove, Arkansas.I
-----------------------------------------------------------------
It appears that this John Burkett is the son of Jackson Burkett b. abt. 1823 and living in Sebastian County, Arkansas in 1860 with a son, John born about 1855. They lived in close proximity to the household of William Thomas Crabtree and Susan Arabella Shipley Reynolds Crabtree in 1870. According to the 1910 census record both John Burkett and his wife Sophronas were previously married. I believe that may be where some researchers have listed her surname as Summers or Summerhill.
1860 Census: Sugarloaf, Sebastian, Arkansas; Roll M653_50; Page: 976; Image: 431.
114 Burkett Jackson 35 1825 Male Arkansas
114 Burkett Mary Anne 23 1837 Female Illinois
114 Burkett Sarah Jane 12 1848 Female Arkansas
114 Burkett George W 10 1850 Male Arkansas
114 Burkett John 5 1855 Male Arkansas
114 Burkett Nancy C 3 1857 Female Arkansas
114 Burkett Sarah C 1 1859 Female Arkansas
1870 Census: Cedar Creek, Crawford, Arkansas; Roll M593_51; Page: 180; Image: 132.
84 Bruhit G W 31 1839 Male White Arkansas
84 Bruhit Angeline 21 1849 Female White Illinois
85 Bruhit Jackson 46 1824 Male White Tennessee
85 Bruhit John 16 1854 Male White Arkansas
85 Bruhit N C 14 1856 Female White Arkansas
85 Bruhit M F 8 1862 Female White Arkansas
85 Bruhit L C 6 1864 Female White Arkansas
85 Bruhit Wm 2 1868 Male White Arkansas
85 Burket Abreham 40 1830 Male White Tennessee
1880 Census:
1900 Census: Upper, Crawford, Arkansas; Roll T623_56 Page: 1B; Enumeration District: 49.
John Burket Head W M Sept. 1854 45 M 25 Arkansas Tennessee Arkansas
Sophroney Burket Wife W F Feb. 1855 45 M 25 12 10 Arkansas Tennessee Tennessee
Marion Burket Son W M Jan. 1879 20 S Arkansas Arkansas Arkansas
William Burket Son W M Apr. 1881 19 S Arkansas Arkansas Arkansas
James F Burket Son W M July 1883 15 S Arkansas Arkansas Arkansas
Jacob Burket Son W M June 1883 14 S Arkansas Arkansas Arkansas
George Burket Son W M Jan. 1887 13 S Arkansas Arkansas Arkansas
Soproney Burket Daughter W F Dec. 1890 9 S Arkansas Arkansas Arkansas
Thurlow Burket Son W M July 1892 7 S Arkansas Arkansas Arkansas
Clementine Burket Daughter W F Feb. 1893 6 S Arkansas Arkansas Arkansas
Jeremiah E Burket Son W M Mar. 1895 5 S Arkansas Arkansas Arkansas
Lockey Burket Daughter W F Dec. 1896 3 S Arkansas Arkansas Arkansas
1910 Census: Upper, Crawford, Arkansas; Roll T624_48; Page: 5A; Enumeration District: 3; Image: 63.
John Burkett Head M W 55 M2 33 Arkansas Tennessee Arkansas
Saphrona Burkett Wife F W 54 M2 33 12 9 Arkansas Tennessee Tennessee
William T Burkett Son M W 27 S Arkansas Arkansas Arkansas
Jacob L Burkett Son M W 23 S Arkansas Arkansas Arkansas
Samuel T Burkett Son M W 16 S Arkansas Arkansas Arkansas
Clementine Burkett Daughter F W 14 S Arkansas Arkansas Arkansas
Ance Burkett Son M W 13 S Arkansas Arkansas Arkansas
Lockys E Burkett Daughter F W 11 S Arkansas Arkansas Arkansas
Arkansas Death Index, 1914-1950
about John Burkett
Name: John Burkett
Death Day: 27
Death Month: May
Death Year: 1915
County: Crawford
Volume Number: 57
Roll Number: 19141923
Certificate Number: 243