If he does well in calculus BC and the AP exam, then he is likely ready for calculus 3 (check the placement recommendations of the college, and have him try the college’s old calculus 1 and 2 final exams). If calculus 3 is taken at a reasonable college and he does well in it, it may not be worth repeating, unless the repeat is an honors course.
Note that math at the upper levels in college will have much more emphasis on theory and proofs (which may have had a tiny taste of in high school geometry). If he ends up preferring the more computational side, then other math-heavy majors like data science or industrial engineering (or some schools’ applied math majors) may be more suitable.
If he does like theory and proofs so much that he wants to go on to PhD study in math, consider whether sufficient upper level and graduate level math courses will be available to him as an undergraduate at each college.