If the lymph nodes in my neck become swollen but i don't have any flu symptoms how likely is it to be cancer?

It depends on their : Painless enlargement of lymph nodes, if it persists for more than 2-3 weeks requires a physical examination by your doctor. Some of these situations are caused by cancer. But it depends on their size and continuting enlargemnt which would make me suspect cancer.

Monitoring Centers: Lymphatic system absorbs/carries things too big to go into the arteries/veins like bacteria eaten by white cells and digested food. Lymph nodes "taste" the lymph for anything bad like bacteria/viruses/cancers, etc. When it detects a problem, it alerts the immune system and your body reacts. They enlarge in response to the inflammation they create when they react. They shrink when all is well.