Coughing is not common in cats. It is most commonly associated with feline asthma in cats. Most cats with asthma show signs of coughing (dry and non-productive), wheezing and laboured breathing. Some cats have a long history of mild cough whereas a small number of cats have severe asthmatic attacks with a sudden onset of wheezing and shortness of breath.
Cats with flu may cough but other signs of flu such as runny nose and eyes and being generally unwell are normally more obvious than any cough. Occasionally owners may mistake their cat's attempts to eliminate a furball from its stomach with coughing. Cats with furballs may retch and bring up only a small amount of fluid at first - the posture they adopt when doing this (crouching with neck extended) can look similar to an asthmatic cat coughing.
If your cat has been coughing for more than 3 or 4 days or is unwell in any other way with a cough contact your vet for advice.