The Gunners won the north London derby without Mesut Özil playing a single minute. The World Cup winner was left on the bench and fellow stars Santi Cazorla and Alexis Sanchez did not start either.
Flamini scored both of Arsenal’s goals while Chambers scored an own goal to briefly level the scores.
The Gunners went into the game having suffered defeats at the hands of both Dinamo Zagreb in the UEFA Champions League and against reigning Premier League champions Chelsea in the Premier League.
Özil was rested for the cup game against Tottenham but is expected to return to the starting line-up against Leicester City on Saturday 26 September at the King Power stadium.
Tottenham 1-2 Arsenal
Kick-Off: 19:45 GMT
Stadium: White Hart Lane
Tottenham Confirmed starting line-up: Vorm, Trippier, Fazio, Wimmer, Rose; Carroll, Dier; Chadli, Eriksen, Townsend; Kane
Arsenal Confirmed starting line-up:
David Ospina; Debuchy, Per Mertesacker, Chambers, Kieran Gibbs; Mikel Arteta, Aaron Ramsey; Alex Oxlade-Chamberlain, Flamini, Joel Campbell; Olivier Giroud