The image below shows one type of flue shroud but there are more depending on fuel type and age of the Aga range cooker. They are fairly similar though and almost all simply lift off the cooker, sometimes with a little wiggling required!
Should you be unable to get the shroud looking good, or if it is heavily chipped or stained, sometimes flue effluent is acidic and marks the enamel, then we sell replacement flue shrouds.
Once you have the shroud off then cleaning it is very simple - pop it in the dishwasher! Dishwasher tablets are mildly caustic which is fine for enamel and it will usually do a very good job. For mild leftover bits try using our cleaning kit and for really stubborn deposits soak the shroud in a strong solution of soda crystals (available from supermarkets) overnight and use a sponge scourer and warm water in the morning to remove the softened muck!