The 78-year-old, of Norfolk Avenue, was the driver of a blue Honda Civic car which left the road at Wardlaw Drive, near where it meets Great Eastern Drive, and collided with a fence.
It happened at about 9.40 am on Sunday and Mr Kennedy was found unconscious in his vehicle.
He was removed by ambulance to Dumfries and Galloway Royal Infirmary were he was later pronounced dead.
Sergeant Leigh McCulloch of the Trunk Roads Policing Unit said: “We would like to hear from anyone who may have witnessed this collision to get in touch with us.
“It does appear that this was a low speed, one vehicle collision and anyone who can help with any information is asked to call Police Scotland on the 101 number.”
The Procurator Fiscal has been informed.
