you cannot combine discounts, it's one or the other. Usually the FD is the better deal. You can book FD through AAA or directly with disney. Alternately, you can book AAA discounts through disney as well (just give them a call and have your AAA card ready).
No, Disney does not allow you to stack discounts. You aren't going to save more than 20% with a AAA discount, probably less. On a value roon that's only about $20.00 per night. A free dining discount at a value resort, for a family of 4, can save you around $100.00 per night.