I think an APO address is just like any other US shipping address, with a zipcode and all, so buyers should be able to provide that type of address like any other.
Or did you want a way to calculate shipping rates differently for for APOs than other US addresses? If you're using one of our USPS live rate-lookup methods, those should work for APOs as well. If you're using a custom rate calculation (Flat or Price Per Unit/Weight), you can create Rules where Country = "United States" and State = "Armed Forces-Americas", "Armed Forces-Pacific" or "Armed Forces-Europe" (this includes Canada, Africa and the Middle East).