We utilize the contra-propagating cavity modes that arise from the evanescent coupling of both the resonators to the bus waveguide in a twin coupled traveling-wave microresonators (MRs) system to generate flat-band slow light (SL). The contra-propagating cavity modes will generate multipeaks in the resonance spectra. Flat-band SL can be generated if such multipeaks become undistinguishable and merge into one single broadened peak that is maximally flat when the inter-resonator coupling strength is optimized relative to the resonators-to-bus-waveguide coupling strengths. The bandwidth and the group delay can be tuned by adjusting the coupling strengths. It is shown that the delay-bandwidth products of the output light at the through (reflection) port are 3- to 12-fold (6- to 24-fold) higher than that of conventional MR-based SL systems. Fabrication tolerance and cavity losses analyses have also revealed that the proposed scheme is rather robust to the fabrication errors and limitations of current state-of-the-art semiconductor processing technology.