I haven't found conclusive documentation on this George's parents. I'm helping a friend with her lines on Geni and I see that Wiki has his father as John but other sites have no parents listed for him at all.
The only Ancestry tree I found with parents listed shows:
George Allen
BIRTH Abt. 1720 Hanover Co., Virginia
DEATH: 30 Jan 1803 Warren County, North Carolina, USA
sources (13) records (12)
Family Info
Father
John Allen (1690–1733)
Mother
Amy Emy (1700–1724)
Spouse
Dianna Powell (1722–1803)
Married 1742
Children
George (1743–1836)
William "Indian Bill" (1750–1816)
Elizabeth (1762–1827)
William (1765–1834)
Dorcus (1767–1805)
Catherine "Caty" (1769–1820)
Jane (1769–)
Sally (1771–)
Thomas (1779–)