The parentage of Robert which appears in old pedigrees is that the father is Kemp-369, and the mother Sherrington-31.
This needs to be corrected, although Jeffrey clearly is a close relative. According to Muskett, Rye, and Hitchin-Kemp, this may be the earliest man in the Kemp pedigree we can be sure of. Hitchin-Kemp does however propose that his father was named John, and not Geoffrey as in some old pedigrees...
"...for Robert, the son of John, not Geoffrey, had grant of the manors of Butteveleyns and Dallings in 1473, as given in Dalry's MSS. (19, 138 add. Mss.) in the British Museum. Although we are unable to give the whereabouts of the original deed, we must credit Dalry's statement that such a document existed signed by "Robert Kempe, son of John." "
(Hitchin-Kemp wonders if Geoffrey and Robert were brothers. Muskett wonders if Geoffrey might be Robert's grandfather instead of father.)
Concerning the mother of Robert, there does seem to be more confidence:
Muskett reproduced an indenture of 1460 concerning the inheritances of the Butvillein family. This shows that Robert Kempe who inherited the manor of Flordon, the advowson and churches of Flordon and Gyssing, and the manors of Hastings and Dallings in Gissyng, together with other properties in Gissing and Norfolk, was son and heir of Alice Kempe.
Alice Kempe was a daughter of Juliana Butvillein, who was a daughter of one Sir Robert Butvillein, and sister of another Sir Robert Butvillein, knight (died 1420).
Hitchin-Kemp proposes that Alice Kemp's maiden name was Alice Duke. On page 12, citing Walter Rye, he states that Juliana Butvillein the sister of Sir Robert married Robert Duke of Brampton in Suffolk, and that it was via her, and her daughter Alice, that the manor of Gissing passed.
So the parents of Robert should apparently be Kempe-181 and his wife Duke-1211. (The old pedigree which places them several generations further back is considered distorted by Muskett, Rye, and Hitchin-Kemp. Possibly this was in order to create room for a wedding with the Hastings family who had held Gissing centuries earlier. But the inheritance of Gissing was through the Butvilleins, and the Hastings had long ago sold the manor.)
The parents of Robert should apparently be Kempe-181 and his wife Duke-1211. Wikitree is currently following an old pedigree which everyone (Muskett, Rye, Hitchin-Kemp) seems to agree is wrong for the early generations.