Yes it is possible to have the flu even without having a fever.
Not all flu viruses are accompanied by a fever and I've had the flu before without having a fever but sometimes the fever can come on later.
Also sometimes even though feel like you have the flu you may actually just have a cold virus instead and not the flu.
With the flu you typically have, muscle aches, headaches, chills, fatigue, sore throat, runny nose and coughing but some people experience some of those symptoms and not all of the symptoms.
But some people may experience all of the symptoms of the flu and it just depends.
Having the flu without a fever is normal and may just be a more mild case of the flu virus.