
No, sorry, it can't be done I'm afraid, for many reasons. DNA swabs can only prove if a dog is the offspring of a dog and bitch who you also have the DNA for - otherwise all it proves is that you have a dog - breeds are genetically far too similar for DNA to prove pure breeding.
Also American Staffordshire Terriers aren't a KC recognised breed in the UK (in fact they're a banned 'type'), so no papers are available at all. Sorry.