Detaching him as son of Sir Thomas Kinne, Kt.. His ancestry is unknown.
Some sources say he came from Scotland, and connect the Canneys with Clan Campbell.
Mabel Demers put forth the theory that Thomas Canney was a son of Sir Thomas Kinne and that his brothers William and John each spelled their names differently. The theory has not found supporting evidence.
Some sources assert he was a brother of Elizabeth Wentworth, wife of William Wentworth (Elder) ~ Immigrant. Both Thomas Canney and William Wentworth lived at Dover, but if they were brothers-in-law, it is unusual that they are not often associated in the records. The only times they appear together is in 1652 and later when they were joint proprietors (with others) of the Fresh Creek saw mill and timber lands.
The sources that identify Thomas Canney and William Wentworth as brothers-in-law often identify Thomas' father as William Quiney, son of Richard Quiney and Elizabeth Phillips. This Quiney family was from Stratford-on-Avon and was connected to the family of William Shakespeare, Bard of Avon.