This man has a research history very similar to John Ellis who also lived in Sandwich. Both may or may not have ties with the Mayflower, but certainly some researchers have insisted they do.
The best write-up for John Vincent is by Harl Preslar Aldrich, Jr. in George Lathrop Cooley and Clara Elizabeth Hall: Their Ancestors and Descendants in America (Rockport, Me.: Penobscot Press, 2001), pp. 213-215. Aldrich claims that John Vincent was in Duxbury by 1637, however, there is no record of him being admitted a freeman there. I'll have to check early land records in Plymouth Colony to see if he owned land there. In any case, John Vincent first appears as a freeman at Sandwich, Mass. in 1643 as "Mr. John Vincent" a title of respect. [Nathaniel B. Shurtleff, Records of Plymouth Colony (1857, reprint 1991), p. 175.] He lives his life in Sandwich and later in Yarmouth, Mass. He has four children, all of whom are captured from their own respective marriage records. John Vincent himself leaves no will or probate. The given and maiden names of his wife is unknown. However, in the Yarmouth Vital Records are the cryptic entries on October 1676 and 5 December 1683 of a "Miss Vincent" dying. These could be unmarried daughters or one may be the wife of John Vincent. [Yarmouth VRs, p. 125]
John's children in order of their marriages and therefore extrapolated births are: (i) Elizabeth m. Sandwich, 8 November 1648 [poss. confused with the next record; first child born in 1649], Thomas Dexter (Jr.) and born say 1625; (ii) Mary m. Sandwich 8 November 1648 [Sandwich VRs, p. 8] Benjamin Hammond, and born say 1627; (iii) Sarah m. 8 July 1653 at Barnstable [Mayflower Descendant 4:223] William Dexter [brother of Thomas above] and born say 1631; and (iv) Henry m. 15 December 1657 at Sandwich [Sandwich VRs, p. 15], Mary Matthews, and born say 1634. The dating of the children is important because you need to be able to date the parents. Based on the above information we can say that John Vincent was married about 1624 and was likely born about 1600.
The faulty research [or the undocumented leap] is that this John Vincent is the son of another John Vincent and Sarah Allerton, sister of Isaac Allerton of the Mayflower and wife of Degory Priest, another Mayflower passenger. In Leiden on 4 November 1611, Degory Priest of London married Sarah Vincent, widow of Jan Vincent of London. [Mayflower Descendant 7:129-30]. Together they have two daughters. Priest dies on 1 January 1620/21 and news of that event is conveyed back to Leiden where his widow remarries in November 1621 to Godbert Godbertson [sometimes transliterated as Cuthbert Cuthbertson]. All four, that is, Sarah, Godbert and her two daughters, arrive in Plymouth in 1623 on the Anne. Both Godbert and Sarah die "without will" before 24 October 1633 when their inventory was spoken of. [Plymouth Colony Records 1:11-13]. Eventually their estate was settled on 3 August 1640 to John Combe and Phineas Pratt who had married the two daughters of Digory and Sarah (Allerton) Priest.
No mention of John Vincent, the man of Sandwich, is ever made in connection with Sarah (Allerton) (Vincent) (Priest) Godbertson, whether in Plymouth or Leiden records. One would have to believe that the younger John Vincent was left in England and Sarah went to Leiden alone. After all the intensive research done on Mayflower families I find it hard to believe that not one record has surfaced that ties the two together in some way. Unlike some theories, here the timeline works. A woman born in 1575 has a son in 1600 and then two more daughters in 1613 and 1615 (when she is about forty) and no more children. Isaac Allerton's birth year is ca. 1586 based on his own deposition and it all holds together.
However, John Vincent is a much more common name than you would think. A search in the IGI for parish records (not patron submissions) shows four John Vincents born in London between 1600 and 1610. If you include all of England and reduce the birth years to 1600 to 1604, there are still 14 John Vincents. Certainly the John Vincent of Sandwich was a man of some social importance. He is a leader of Sandwich from the beginning and given the honorific "Mr." in town records. Further research is needed in England to find his origins. However, for now, his connection with Sarah Allerton is based solely on her marriage record as a widow of John Vincent. Intriguing? Yes. Evidence? No. Certainly not anywhere close to being a reasonable determination of a relationship.