Sadly, the answer is no. BA miles can only be used to upgrade BA flight numbers on BA metal (or a franchise partner). They cannot be used on any other OW member airlines, nor on Air Tahiti Nui.
Your best bet would be to look at a cash upgrade at check in (I believe thwy offer this but I could be confusing with Air Pacific). If you have any, you might be able to use QF miles, but the lovely people on the QF board will help you with that.
FWIW, there are a fair few threads on the AA board about Air Tahiti Nui. Might provide some nuggets.