The answer was given in a comment:
After your Qa5+ how do you make White play Kf1? What do you do if he plays Qd2?
This is correct. There's really nothing you can do after Qa5+ Qd2 that gives Black a significant advantage.
He can play Qd2 after Bxa3; Nxa3 Qa5; too right?
White can play that, but it doesn't help in that position. You can take the knight with your queen. (If you played Qa5+ first, then ...Qxa3 loses to Nxa3, and ...Bxa3 is obviously responded to with Qxa5.)
[FEN "rnbqkb1r/pp4pp/2p1pn2/3p1p2/3P4/BP4PN/P1P1PPBP/RN1QK2R b KQkq - 0 1"]
[startflipped ""]
1... Bxa3 (1... Qa5+ 2. Qd2 Qxa3? (2... Qxd2+ 3. Kxd2 Bxa3 4. Nxa3 {Material is even.}) (2... Bxa3 3. Qxa5 Bb2 4. Qb4 Bxa1 {Rook and bishop for the queen for now, although Black's bishop may get trapped. Certainly White has the advantage.}) 3. Nxa3 Bxa3 {Two pieces for the queen; White is clearly ahead.}) 2. Nxa3 Qa5+ 3. Qd2 Qxa3 {Black is up a knight.}