No, sore throats are more often caused by the virus of the common cold and not the flu virus.
If during the fall and winter (in the Northern Hemisphere) during flu season, it may more likely be the flu, however. See the related question below about the differences in symptoms between the common cold and the flu. The flu season is in the spring and summer in the Southern Hemisphere.
Sore throats are also often caused by bacterial infections, like "strep throat". If you do not have the other symptoms of the flu or a cold with a sore throat, this may be the cause. Often a health care professional's exam is needed to determine which it is so that the proper treatment can be started.
Don't smoke cigarettes, then the sore throat could be due to irritation or even cancer.