Brother is being discharged for having ADHD in his past. What happens now?

Here is what happened. He went to MEPS and never mentioned having ADHD. If he had he would have had to of gotten a waiver to enlist. Some of these comments are nonsense. There is no 1 year rule then you don't have to tell MEPS. While at training for whatever reason he told the DI or another Cadre or medical that he had taken this medication. It happens all the time. As a result he will now receive a training discharge more than likely uncharachterised. As for him going home, he is currently serving in whats called a holdover company or platoon where he is doing various details until the Army decides to cut orders. This can take a week or a couple months. I have seen kids in this scenario end up being there longer then the class they they were training in. No you do not go there to pick him up the Army will put him on a bus once the orders are cut. Be patient.

If he's being separated for ADHD in Basic it means that he had a behavioral health issue arise that was tied to his previous diagnosis. These separations take time, it's not a priority for the Cadre

As a former Drill SGT from Sand Hill, FT Benning, I have seen this many times.
If the trainee states he told the recruiter about the ADHD, they will investigate it. But that doesn't clear the trainee. He was asked several times at MEPS to divulge any info asked for, even if the recruiter told them not to.
At the Company level in Basic he will be pulled from training and put in the holdover section with injured trainees, disciplinary trainees, and the "refuse to train" trainees until processing is complete and he's separated, it's a bit of paperwork and legal is involved. I have seen these cases go well beyond the end of the cycle and the trainees get passed around to the next company with holdovers/chapters.
Your brother will be pulling details while in holdover and I will be honest with you its not a good situation. He needs to be where he's told to be at the time he is told and in the proper uniform. The DS's will leave him alone if he isn't the squeaky wheel. Trust me as a DS I was spending most of my time on the disciplinary cases and the trainees that were just in a bad place I left alone and made sure they were good.
And as far as not hearing from him goes, phones are a privilege and the 1SG determines "if" the holdovers get use of their phones.