There is no particular season for duct cleaning. And there is no best time as such. If you notice any kind of smell through your ducts or if you feel that the air flow is not as good as it used to be then it is an alarm that your ducts need professional help. Also, if you have been noticing more sneezing and coughing in the house then your ducts might be in a bad shape. Moreover, an increased power bill could also be because of dirty ducts.
It is recommended to get your ducts cleaned once in every season so that they keep on working fine.