Note: The regular commercial flight operations to Mysore is suspended.
Though there are no flights to Mysore, both Chennai and Bangalore are superb connection point for many destinations from Mysore, as both Bangalore and Chennai are some of the busiest international airports in India.
If flight is not an option, you can travel from Chennai to Mysore by train and bus too.
You best bet to reach Mysore from Chennai is Kaveri Express and Shatabdi Express.