A couple of items in your posting are not clear. According to the book "Some Descendants of John Burk (1656-1699) Middlesex County, VA", Henry Burk (1758-1840) was born in Caroline County, VA. He was a private in the Revolutionary War, and has been confused with his cousin Capt. Henry Burk.
Henry Burk's parents Thomas Burk, Sr., born c1731-1732 in Caroline County, VA; died after 1812 in Franklin Co., GA; and Ann George, daughter of Robrert George, Jr. of Caroline County.
These people are the ancesters of the immigrant, John Burk who was born before 1633 in England (not Ireland) and came to Lancaster County, VA c1650. He died by 1659.
History has documented that the 2nd wave of English settlers came to VA from the South of England between 1642 and 1675 (See "Albions Seed - Four British Folkways in America" by David Hackett Fischer (Oxford University Press, 1989) pp207-418. While a few Irish immigrants trickeled into America in the 17th century the peak period in the 4th wave, along with North Britain from 1717 to 1775. This wave settled mainly in American back country.