My general recommendation is that if the student has AP credit that the college allows skipping courses with, and the student wants to take a course where the skipped course is a prerequisite, the student should try the old final exams of the course that can be skipped to make a more informed placement decision. (As reply #11 mentions, some colleges have their own mandatory or advisory placement tests to do this type of thing if they do not want to rely solely on AP scores.)
Otherwise, the student is just guessing, and the consequences of guessing wrong are undesirable – either wasting time and tuition repeating something the student already knows instead of learning something new, or struggling with the more advanced course due to insufficient prerequisite knowledge.
As a CS major, he is likely to need math courses that have calculus 2 / calculus BC as a prerequisite, so the try-the-old-final-exam recommendation applies here. But he is less likely to need courses that need general chemistry / AP chemistry as a prerequisite unless he wants to do pre-med* or another major in chemistry or biology or something like that, so he may not need to worry about this question with respect to chemistry.
*Note: medical schools do want to see enough pre-med courses in college, often not accepting AP credit for them, but often accepting more advanced courses if some are skipped with AP credit (but some dislike the common practice of repeating AP credit, which can be seen as grade grubbing). Since different medical schools differ in policies, that is a more complicated question that should be asked in the pre-med forum section if there is any pre-med intention.