 Wynne was educated at Jesus College, Oxford, matriculating in 1668 and obtaining his Bachelor of Arts degree in 1672.He later obtained a doctorate in law and seems to have become a member of Doctors' Commons in 1694.When the Welsh lawyer and academic Sir Leoline Jenkins – who had been the Principal of Jesus College during Wynne's time in Oxford – became Secretary of State for the Northern Department in 1680 (and later Secretary of State for the Southern Department), Wynne became his confidential secretary.