Are you talking about a specific person or just people in general? At the moment you are only talking about one specific man.
Anyway, if one specific man:
This person (man/patient? might be better than 'person') should not have a flu vaccination if he has a chronic illness and is showing symtoms at the time of vaccination.
This person (man/patient?) is should have a flu vaccination if he has a chronic illness but no symptoms at the time of vaccination.
A lowering of the platelet count is a reaction to a flu shot. The lowering is temporary and the platelet count will return to the normal level in a short period of time.