The service said firefighters had extinguished all remaining hot spots at the scene and that an investigation into the cause of the fire was under way.
The fire service had been joined by crews from Kent Police, South East Coast Ambulance Service and Air Ambulance Charity Kent Surrey Sussex in responding to the blaze.
People living nearby or travelling through the area had also been urged to close windows and doors due to the smoke.
Kent Police and South East Coast Ambulance Service have been contacted for more information.
