His grandfather, also Robert Wynne, had been mayor of Canterbury in 1599, and other relatives had served in Parliament.
He served on the county court, though he was fined for poor attendance in September 1659.
[2] The House of Burgesses called by Sir William Berkeley in 1661 continued without dissolving until 1676, meeting in seventeen sessions during that period.
At the second session in 1662, Wynne was elected as Speaker to replace Henry Soane, who had died during the recess.
Under Wynne's leadership, the House took an active role in business previously left to the Governor and Council, creating a standing committee to advise the Governor between sessions.