Children according to one source:
1.  William THOMPSON
2.  Benjamin THOMPSON
3.  Lewis THOMPSON
4.  Elizabeth THOMPSON
5.  Martha THOMPSON

1a.  Jordan R. Dodd, et al.  [nd]  Early American Marriages: Virginia to 1800.  Precision Indexing Publishers, Bountiful, UT (online at Ancestry.com):

Thompson, James Mims

Jackson, Nancy

3 Jan 1789

Mecklenburg Co., VA

1b.  Email.  Consent for James to marry is given by "John Thompson" (no relationship given).  Consent for Nancy to marry is given by Fleming and Elizabeth Jackson, said to be her "parents," but Fleming is her older brother.  John Allen gave bond.

2.  Census Index:  U.S. Selected Counties, 1790 (Broderbund CD-311):  not found, but the 1790 VA census was destroyed.

3.  Census Index:  U.S. Selected Counties, 1800 (Broderbund CD-312):  not found, but the 1800 VA and KY censuses were destroyed.  James M. Thompson does not occur on the tax rolls of Christian Co. until 1806, so he was not in Christian Co. in 1800.

4.  1810 Census Index/Images (online at Ancestry.com; Image #7 of 66; extracted by Diana Gale Matthiesen; see 1810 Table): 

1810

KY

Christian Co.

p. 59/519

Ln. 1

James M. Thompson

31211-11010-00

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
3 males	9 or under	1800-1810	= William (b. ca. 1805) = James Jr. (b. ca. 1803) = John (b. ca. 1800)
1 male	10-15	1794-1800	= Fleming J. (b. ca. 1797)
2 males	16-25	1784-1794	= Sanders (b. ca. 1792) = Lawson (b. 1790)
1 male	26-44	1765-1784	= James Sr. (b. 1769/71)
1 male	45 or over	in or bef. 1765	= ?
1 female	9 or under	1800-1810	= Sarah (b. ca. 1807)
1 female	10-15	1794-1800	= Elizabeth (b. ca. 1794)
1 female	26-44	1765-1784	= Nancy (b. 1770/74)

James's father and Nancy's father both died in Virginia, so who is the older male?

5.  1820 Census Index/Images (online at Ancestry.com; Image #7 of 23; extracted by Diana Gale Matthiesen; see 1820 Table)): 

1820

KY

Christian Co.

p. 34

Ln. 23

James M. Thompson

111002-11001-0-400

1000-1010

These data indicate:

No., Race, Gender	Age Class	Therefore Born	Individuals Inferred
1 white male	9 or under	1810-1820	= Son A
1 white male	10-15	1804-1810	= William (b. ca. 1805)
1 white male	16-18	1801-1804	= James Jr. (b. ca. 1803)
2 white males	45 or over	in or bef. 1775	= James Sr. (b. 1769/71) = ?
1 white female	9 or under	1810-1820	= Daughter A
1 white female	10-15	1804-1810	= Sarah (b. ca. 1807)
1 white female	45 or over	in or bef. 1775	= Nancy (b. 1770/74)
4	people engaged in agriculture
1 male slave	13 and under	1806-1820	= ?
1 female slave	13 and under	1806-1820	= ?
1 female slave	26-44	1775-1794	= ?

The "mystery" man is still with us.

6.  1830 Census.  Where is he?  He's not in Christian Co., KY, or Polk Co., MO.  There is a James M. Thompson in Trigg Co., KY, but he is also there in 1840, so he cannot be our subject.

7.  1840 Census Index (online at GenealogyLibrary.com):

Thompson, James M.

MO

Polk Co.

2nd Division

p. 184

8.  From The Kentucky Land Grants by Willard Rouse Jillson (1925, Filson Club Publ., Louisville, KY; reprinted 1994 by Genealogical Publ. Co., Baltimore, MD; online at Ancestry.com).   Tax records indicate that the 45 a. and 200 a. parcels belong to our subject, James Mims Thompson, so "James N." is a mistake somewhere along the line.

Name	Acres	Date	Watercourse	County
Thompson, James N.	45	3 Jan 1807	Tradewater	Christian
Thompson, James N.	200	2 Jan 1807	Barren Fk, Tradewater	Christian
Thompson, James M.	100	7 Sep 1810	Tradewater	Christian
The Tradewater River runs from north central Christian Co. northwestwards to become the boundary between Hopkins and Caldwell Cos.  I have yet to locate the Barren Fork of the Tradewater.

9.  Anon.  1993.  Christian County, Kentucky, Wills and Estates, 1815-1823: Christian County Will Book C.  T.L.C. Genealogy, Miami Beach, FL.

p. 46	Page 166.  This day, Laurence Brashier, James Clark, James M Tomson, were qualified to settle the acct between Powers Lamkins, administrator of the estate of William Lamkins decd, this Sep 7, 1818.  Signed - Jonathan Clark, JP.
p. 116	Page 473.  Inventory.  Agreeable to an order of [Christian County] Court at their Sep Term, we appraised the estate of Nathaniel Brown deceased, or such part thereof as was presented to us, and
p. 117	find it to be worth $642.77½.  Signed Sep 27, 1822 - Benjamin Armstrong, John Armstrong, JM Thompson.  Recorded Dec 2, 1822.
p. 130	Page 528.  Per [Christian County] Court order at their present term, we were appointed to settle with James M. Thompson, administrator of William Lampkin (Lampkins), deceased his account.  We examined the papers and records in sd case, and upon examination of the same and the receipt of sd James M
p. 131	Thompson, we find that they agree, that is, the accts balance and sd James has proven in full, all demands to sd estate.  Signed Jun 2, 1823 - John Bradley, William Williams.  Recorded Jun 2, 1823.

10.  Christian County Genealogical Society.  1997.  Christian County, Kentucky, Deed Abstracts of Books G-H-I (1816-1819).  Christian Co. Gen. Soc. (1101 Bethel St.), Hopkinsville, KY 42240.

p. 135

DBI-420, Oct. 7, 1818.  from WILLIAM WATERS of the State of Indiana, to JAMES M. THOMPSON, for $400.00, 200 a. on TRADEWATER, bounded by the meandering of the river, James M. Waters line, & others.  S/William Waters, EASTHER WATERS,  Wit:  Lofton (his X mark) Thompson.  Dower relinq.  Rec. 7 Oct. 1818.

11.  LDS.  Family Search: Internet Genealogy Service: Ancestral File.

12.    Family Group Sheet No. 54975:  James Mins Thompson.  Everton Publishers, Inc.  (Broderbund CD-14).

13.  The Last Will and Testament of John Thompson, Sr. 

14.  Emails from Marsha Videen, Sherry Yancey Babb, Hilda Hood.

There is somewhat of a controversy over the James Mims THOMPSON who married Nancy JACKSON.  One source believes he died in Virginia in 1819, the son of "John THOMPSON, Sr."  Other sources believe he is the above James M. THOMPSON who moved to Christian Co., KY, later died in Polk Co., MO, and was the son of John and Sarah [ALLEN?] THOMPSON.  It seems that another source finds "John THOMPSON, Sr." and the "John THOMPSON" who married Sarah [ALLEN?] to be the same person.   The crux of the matter  lies over the issue of whether the "James M. THOMPSON" mentioned in the will of John THOMPSON, Sr., was dead or alive when the testator wrote his will in 1829 and, if alive, is he the James Mims THOMPSON in Christian Co., KY?