- He is SAR P-173800, born 1743 and died 1810; the only child listed in the SAR is Samuel.
John Sr. came from Northern Ireland and landed in Baltimore in 1763 or ‘64, having met Elizabeth on board the ship.
He is identified in the directories for the SAR as a Sergeant in the PA Line. He fought in the Revolutionary War under Captain Isaac Seeley, 5th Pennsylvania Regiment, commanded by Col. Francis Johnston. [This may be an error; it may be the John Hamilton d. 1818 who served in this regiment.]
Frazee (S22) records a variety of documents relevant to his pension application and will, including some testimony of his war experience, on 565-81. He is included on the Revolutionary War page.
He moved his family to Bracken Co., Kentucky in 1797. He appears on 22 Nov. 1799 as John Sr. on the Bracken County census.
One other source: Donna Jean (Hamilton) Cochrane, "Hamilton: Early Kentucky Settlers, Bracken Co." Donna Cochrane died in 2001.
Lizzie Mannen Turney's DAR Application reaches back to John Hamilton who fought in Capt. Seeley's company. A later note  by a DAR researcher has been typed on the application saying this: "This John Hamilton was a private in Captain Thomas Paxton's Co. of Bedford County, Pa. Militia, 12-18-1776. See Pa. Archives, 2nd Series, vol. 14, p. 653-5. The [sic] John Hamilton was born 1755 and died in Indiana Co., Pa. See Pa. Archives, 2nd Series, vol. 10, page 549." As far as my research tells, this note is in error.
Note that there is also a John Hamilton, who died in Indiana Co., Pennsylvania in 1818, who was also a Revolutionary War veteran; he was not from this family.