"I've got the Flu" means that you caught it and at the moment you're still having symptoms of it. On the other hand "I had the flu" means that you were sick and at the moment you're feeling well again. Ich hoffe, dass diese Erklährung hilfreich ist.

I've got the flu means right now. I had the flu is in the past. I teach English classes. Let me know if you are interested in booking a class.