Exercising and getting your body where it's sweating can help you feel better and the sweating and exercise is good for your health and can help relieve some symptoms of the flu.
I do find that when I exercise and get sweaty that the flu seems to go away sooner and I feel much better instead of just laying around on the couch or in bed until the flu goes away.
But there's no way to actually sweat out the flu virus because for the flu to go away the virus that causes the flu has to go away or be killed off.
Sweating won't get that flu virus or even cold virus out of your body so you'll still be sick but when you sweat and exercise your boost your bodies immune system which helps to fight off that flu and cold virus.
So while you're not sweating out the flu or cold virus you are helping to kill the flu or cold virus sooner because you're boosting your bodies immune system and sweating and exercise is good for your health.