You must realize that dimension table don't store all possible dimension values - they store only those that were already used. Therefore you want find the data you need in dimension tables.
You would have to use the tables (such as cost centers) directly and reimplement a huge amount of AX logic (if you want to respect all rules defined in account structures and so on). It looks like a huge waste of time. Rather then reimplementing it in SQL, just reuse the existing functionality - expose it as a web service.