I agree he should take those HS Chem classes and the Chem AP test after the class.
He would also be well-advised to take whatever Physics they have, assuming it fits his schedule overall, meaning without sacrificing other core areas unduly.
Beyond that, I think the purpose of self-study is really for interest sake, and possibly also better preparation for college classes. Doing it for credit is likely going to be covered by the AP class and test. Any sort of documentation beyond that probably won’t have any credit benefit. I note the Chem department may also have its own placement test, in which case placement will be a matter of what he actually knows.
And I think the same is largely true for admissions as well. Like, it will be fine if he communicates an interest in self-studying Chemistry in his application in one or more ways. If that naturally leads him to things like olympiads and internships, great.
Admissions will then not need to see that interest also reflected in things like self-study AP tests. So, no need to get ahead of the standard AP process for that sort of purpose.