If she really had the flu I doubt that she would be feeling well. The school would notice and send her home. I would expect any child with an infectious disease not to attend school.

A cold or runny nose I would send if they felt ok. Just as I go to work with a cold. If it was really bad and they were not feeling well they would stay home.

If you have reason to believe the child had an infectious disease, I would advise the teacher.

ETA if I didn't send them every time they had a cold, they would only be in school about a quater of the time!