@RubioRic's answer is correct to a degree. Most people colloquially refer to the illness as "the flu", however as you can see from the dictionary quotation he cites you can refer to "a flu virus". It would be medically incorrect to say "the flu virus" unless you had already defined a specific virus that you were speaking about. It is too simplistic to say that "the" should go before "flu" and never "a".
There are many different strains of flu (or influenza to use its proper name) and these are caused by distinct influenza viruses. As these viruses are countable then these would be referred to as "a flu virus" or "an influenza virus".
It is also common to omit "the" altogether and simply say:
I have flu.
The British National Health Service page on flu uses both "the flu" and simply "flu" in the same article, but with a clear bias towards the latter:
"Flu is very infectious.."
"GPs don't recommend antibiotics for flu.."
"How to treat flu yourself"
It does contain one use of:
"The flu vaccine..."
but this is referring to the vaccine, not the flu.
And with specific new strains of flu being diagnosed in recent years these are sometimes referred to by their proper names, even outside the medical profession, such as H1N1 (commonly referred to as swine flu) or "bird flu". Interestingly these are never referred to as "the swine flu".
The use of "the" when referring to an illness is somewhat of a legacy and not always used. You don't hear people say "I have the headache" - we say "a headache" despite the fact we only have one head. Neither do you hear people speak of (relatively) recently diagnosed conditions this way, such as "the AIDS" (not correctly used to my knowledge). It tends to be restricted to diseases that were historically described that way for example the pox (an archaic term for syphilis that dates from late middle English but was still commonly used as late as the 1970s in British English), or even the plague.