"The patient has the flu."
Translation:De patiënte heeft griep.
Is it the common rule in Dutch, that you don't add definite article (de/het) before the illnesses?
Yes (when I think of other ilnesses - maybe there are exceptions that do not come to mind now).
With most illnesses you don't add de/het, but with the flu, you can both say 'hij heeft griep' or 'hij heeft de griep'. Personally I hear the last one being said much more often, but both are ok.