Generally speaking, evidence of previously having had chickenpox is considered evidence of immunity, in the same way vaccination is. A blood test that shows the antibodies are present will also normally meet the test. They just need to know the kid is unlikely to get the disease even if exposed. Vaccination, previous illness, or proven antibodies in a blood test all provide that assurance and mean exclusion from school is not required.
Note, that with these kids, a blood test would let them go to the prom. Unfortunately, it seems that the turnaround time for such test results isn’t fast enough.
Just because you’ve had the chickenpox once doesn’t mean you can’t get it again. About 10% of the population can get it again. I’ve had it 4 times. Each time it was less severe.