If you are asking who is the father of Nicholas Kellogg, then there is no simple answer and it is unlikely to be found in any book.
There are two possibilities: Debden and Bocking, both in Essex.
In Debden, Nicholas Kellogg (or Kylogg, Kelhog, etc) is first mentioned in the will of his father-in-law, William Hall, in 1515. Nicholas is recorded in lay subsidy and muster rolls in the 1520s and 1530s. There is also a William Kellogg recorded as a witness to deeds and in the same lay subsidy and muster rolls from 1518 until 1536. The two are probably related, but whether they are brothers, father and son, or distant cousins I don’t know.
There had been people named Kellogg in Debden and nearby for a long time. For example, there was a John Kilhogge, of Debden, husbandman, in Common Pleas in 1430. There was a William Kylhog, of Wimbish, husbandman, son of Thomas Kelhogg, of Radwinter, (both within a mile or two of Debden), recorded in Common Pleas 1428 to 1433. These might have been the ancestors of Nicholas and William Kellogg, but there isn’t enough evidence to prove it.
On the other hand, it could be that the ancestry of the Kellogg family in America was in Bocking, Great Leighs and elsewhere near Braintree, about 20 miles from Debden. The first certain ancestor is Philip Kellogg, who was in Bocking in 1583 and in Great Leighs in 1585. Philip, according to The Kelloggs in the Old World and the New, (Timothy Hopkins, 1903) is “probably son of Thomas”, but “There is a missing link in the chain of documentary evidence connecting the families of Bocking, Great Leighs and Debden.”
So it is possible that the Kelloggs had been living around Braintee all along. In 1560 and 1561, when Thomas Kellogg the presumed father of Philip was still in Debden (he is recorded there in 1568 and 1571), another Thomas Kellogge and his wife Marion were in feet of fines concerning land in Ulting, Hatfeld Peverell and Boreham. These parishes are about 6 miles south of Braintree and 2 miles from Great Leighs. There is a farm called Kilhogs Farm in the parish of Shalford, just north of Braintree and about a mile from Bocking. It is shown on maps going back to the beginning of the 19th century. There was a Walter Kelhogg, of Shalford, husbandman, in 1418, and a John Kylhogge, of Bocking, husbandman, in 1446, both recorded in Common Pleas.
But for both of these possibilities, Debden and Bocking, there is a gap of at least two or three generations.
https://archive.org/details/kelloggsinoldwo03hopkgoog/page/n6
http://esah1852.org.uk/images/pdf/ffines/F1500000.pdf
https://sites.google.com/site/meadfamilyhistory/home/legal-records/kellogg