Using The Seven Times Rule:
"When two or more appliances are connected to a chimney, the flow area of the largest section of that chimney cannot exceed seven times the smallest flue collar, or draft hood outlet area, unless designed with approved engineering methods."
the largest diameter of the chimney flue liner would be 7″. Assuming that the furnace’s vent pipe has been improperly downsized (you’d have to check with the manufacturer / some types of furnaces permit 1″ downsizing), the smallest diameter would be 6.5″ (largest diameter + 50% of the smallest).
Since they don’t make 6.5″ diameter vent pipes the closest one is 7″ or 6″ if the downsizing of your furnace vent pipe would be permitted. If by any chance you’re in a cold climate, make sure you have insulated liner installed.
You can find more information about this subject by visiting chimney flue size post