I am sorry to have to bear bad news. If he was discharged with an honorable discharge, it is unlikely he can do much of anything
This is based on the rules surrounding the administrative discharge
The services, including the Air Force, have great latitude in setting the rules for separation of service members. The Air Force rules are contained in Air Force Instruction 36-3208. This regulation (which used to be available online...before the Air Force removed it) allows the Air Force to separate an Airman if they are not able to meet academic standards
So for your son, in order to be reinstated, he would need to prove, in essence, that he did meet academic standards
He can apply to the Air Force Board for Correction of Military Records. This agency has the power to change records, and can even order a service member to be reinstated. But the burden of proof lies with the servicemember. Your son would need to prove that he met academic standards.
And he would need to provide evidence to support. The Air Force Board for Correction of Military Records gives a presumption of regularity to the service...they presume the unit got it right. The applicant must present evidence to overcome this presumption.
So unless he can prove he met academic standards..basically, prove he did not fail the test, he will not be able to get back in
I am very sorry to have to bear bad news
Let me know if you have more questions.