I have yet to figure out when the records refer to Paul I or Paul II, except that Paul I is not mentioned in his father's 1667 will, so Paul I presumably died before 1667 and all records after that date would presumably refer to Paul II.

Elizabeth may be the wife of Paul KINSEY II, not Paul KINSEY I.

WARNING:  There is no proof that Paul II and Margaret are Paul I's children, they are merely listed as grandchildren in Hugh KINSEY's will.  However, the only other known son of Hugh KINSEY was Daniel KINSEY, about whom there is nothing in the records after his transport to Maryland by his father in 1662, suggesting Daniel died not long after arrival in Maryland and leaving Paul I as the only obvious parent of any Hugh KINSEY grandchildren surnamed KINSEY.

1.  George Cabell Greer.  1912.  Early Virginia Immigrants, 1623-1666.  W.C. Hill Printing Co., Richmond, VA (republ. 1978/82 by Genealogical Publ. Co., Baltimore, MD; Broderbund CD-354):  These are not immigration dates, but dates of mention in Virginia land records.  Paul is the only Kinsey listed by Greer.

p. 194

Kinsey, Paul

Virginia

1655

It's doubtful Paul could have been a minor at this point, so that puts his birth in the 1630s.

2.  Nell Marion Nugent.  1934.  Cavaliers and Pioneers: Abstracts of Virginia Land Patents and Grants, 1623-1666.  Vol. 1.  Dietz Printing Co., Richmond, VA (reprinted 1983, Genealogical Publ Co., Baltimore, MD; Broderbund CD-354).  These are not immigration dates, but dates of mention in Virginia land records.

p. 325	Kinsey, Paule	Virginia	1655
p. 458	Kinsey, Paul	Virginia	1664
p. 266	Kinsey, Paul	Virginia	1683
p. 266	Kinsey, Jon	Virginia	1683

The Paul KINSEY in 1683 is presumably Paul II because Paul I appears to have died before his father, Hugh KINSEY, signed his will in 1667.

3.  Gust Skordas, ed.  1968.  The Early Settlers of Maryland: an Index to Names of Immigrants, Compiled from Records of Land Patents, 1633-1680, in the Hall of Records, Annapolis, Maryland.  Genealogical Publ. Co., Baltimore, MD (Broderbund CD-354).  These are not immigration dates, but dates of mention in Maryland land records.

p. 276

Kinsey, Paul

Maryland

1661

4.  Robert W. Barnes.  1989.  Baltimore County Families, 1659-1759.  Genealogical Publ. Co., Baltimore, MD (Broderbund CD-195):

p. 387

KINSEY, HUGH (1), imm. to Md. c. 1659; in 1662 he transp. his ch. Daniel and Sarah; in Aug. 1663 he surv. 100 a. Walnut Neck which was later held by Isaac Jackson (45 a.) and John Wilmot (55 a.); d. leaving a will made in A.A. [Anne Arundel] Co., 6 May 1667, naming

p. 388

Sara Clark and Charles Gorsuch, w. Margaret, dau. Eliza Kinsey, Mary Humphreys, and Grandch. Paul and Margaret Kinsey and Hancock Ball; had iss.: DANIEL, transp. in 1662; SARA, transp. in 1662, m. by 1667 (Abraham) Clark; PAUL; and ELIZA... KINSEY, PAUL (2), s. or grandson of Hugh (1), was named as a s. of Margaret Kinsey in 1661; on 31 March 1662 surv. 100 a. Spring Point, which Paul and Elizabeth Kinsey conv. to William Gwynn on 5 Feb. 1663; on 2 April 1662 he surv. 200 a. Curtis' Neck and on 18 Aug. 1663 he surv. 350 a. Harborough; alive on 10 April 1672 when he surv. 200 a. Paul's Neck, later held by John Lockett for the orphans of Richard Gwynn...

Hugh KINSEY appears to have had both a son and a grandson named Paul.  However, Paul KINSEY, s/o Hugh KINSEY, had to have died before Hugh wrote his will 6 May 1667, so any records after that date — and possibly some before that date, as well — must refer to the grandson.

5.  George Cabel Greer.  1912.  Early Virginia Immigrants, 1623-1666.  W.C. Hill Printing Co., Richmond, VA (online at Ancestry.com).  On p. 194:

Kinsey, Paul, 1655, by Mr. Hugh Kinsey, Lancaster Co.

Records are said to be taken from land records, with the name of the sponsor given.

6.  Jane Baldwin, ed.  1988.  The Maryland Calendar of Wills. Vol. I.  Family Line Publ., Westminster, MD (Broderbund CD-206).  "A.A." = Anne Arundel.  On p. 40:

Kinsey, Hugh, A.A. co., 6th May 1667; To grandson Paull Kinsey, "Walnutt Neck." To Sara Clarke, grandchildren Hancock Ball and Margaret Kinsey, and Charles Gorsuch, personalty. To wife Margaret, residue of estate, real and personal. To young. dau. Eliza: Kinsey and hrs., said estate at death of wife afsd. In event of death of said Eliza: without hrs., estate to pass to Mary Humphreys, at whose death, sd. estate to be divided among rest of testator's children, equally. Test: Wm. Hare, John Malom. 1. 291.

Sons Paul and Daniel must be deceased.

Grandchildren Paul and Margaret KINSEY are presumably children of Paul and/or Daniel, or possibly some other son unknown to us.  I'm inclined to believe they are the children of Paul KINSEY because, other than his being transported in 1662 by his father, there is no mention of Daniel anywhere in the records, which suggests he died early on.

7.  John Davis.  1996.  Baltimore County, Maryland, Deed Records, Volume One: 1659-1737.  Heritage Books, Bowie, MD.

p. 94-95	13 Feb 1664, Richard BAll, of Patapsco, Baltimore Co., Maryland, to Rowland Haddaway, two tracts, 300 acres... Bear creek and Humphrey's creek... and warrant from heirs of Thomas Humphreys, deceased. Signed Richard Ball. Wit: John Gwyn and Paul Kinsey.
p. 86	26 Apr 1671, Evan Gwin, planter, of Maryland and John Gwin, planter, of Virginia, to Charles Gorsuch, of Baltimore Co., Maryland, 2000 pounds of tobacco, 100 acres... Patapsco River... patented by Paul Kinsey. Signed Evean Gwin and John Gwin. Wit: Bening, Hugh Montgomery, John Parsons, John (x) Gray and Robert Burgen.
p. 27-28	[no date, but among deeds mostly ca. 1689] George Yate, gentleman, of Anne Arundel Co., Maryland, to Thomas Hooker, planter, of same, £63, 230 acres.. line of the Orphan Kinsey. Signed George Yate. Wit: Richard Hanslap, James Ellis and John Elsey.

An "orphan" was someone whose father had died (the mother might still be alive).  Was this in reference to Paul Kinsey?  Other references to George Yate and Thomas Hooker do not mention any Kinsey.

8.  Anon.  1999.  Anne Arundel County, Maryland, Land Records, 1728-1730.  T.L.C. Genealogy, Miami Beach, FL.  Abstracts from Anne Arundel County Circuit Court Land Records Book TI #1.  "AA" = Anne Arundel Co.

p. 39

Page 152.  Dec 16, 1729 from William Robinson of AA, planter, to William Chapman of AA, Merchant, for 32 £ 9 shillings and 3 pence sterling, all that piece of land lying on the south side of Potapscoe River, and on the north side of a creek of the sd river called Coxes Cr in AA, and being the remaining

p. 40

part yet unsold, of a tract of land called Brandon, originally granted to Paul Kinsey, and which, by diverse alienations and mutations of possession, is now become the proper right and estate of the above sd William Robinson, which land to be hereby sold is bounded by the high water mark on the north side of the afd Cockses Cr, the original survey of Brandon, a parcel of land formerly sold by the sd William Robinson to Thomas Joyce, then to Wells' Pond, containing about 100 acres.  Signed - William (WR his mark) Robinson.  Wit - Mord:a Hammond, Walter Dallas, Geo: Neilson, Turnor Wootton.  Ack. before Benj:a Tasker, a Justice of Provincial Court. Recorded Mar 5, 1729/[30].