There is growing interest in the use of short-pulse lasers for coherent anti-Stokes Raman scattering (CARS) to minimize non-resonant background (NRB) contributions in a variety of applications. Using time-coincident picosecond (ps) pump and Stokes beams and a time-delayed ps probe beam, we show that a three orders of magnitude reduction in NRB interference can be achieved in rich hydrocarbon-air flames while preserving 60% to 80% of the CARS signal. This represents a significant improvement in signal-to-interference ratio compared with previous measurements in room temperature air and is attributable to reduced rates of collisional dephasing and relaxation at flame temperatures. Measurements within the flame zone of a laminar flat-flame burner are used to investigate the characteristics of time-coincident and probe-delayed broadband ps N(2)-CARS spectra for C(2)H(4)-air equivalence ratios of 0.5 to 1.2. Up to three ro-vibrational bands of N(2) are excited with each laser shot using 135 ps pump and 106 ps Stokes beams, and the CARS signal is generated using a 135 ps probe beam delayed by 165 ps. The enhanced signal-to-interference ratio achieved in the current work is one to two orders of magnitude higher than that previously achieved using polarization-selection techniques without sensitivity to the effects of birefringence caused by density gradients or test cell windows. Moreover, the use of a 135 ps laser source in this study enables frequency domain "broadband" CARS with sufficient resolution to extract ro-vibrational spectral features under various flame conditions. The effect of probe delay and NRB suppression on characteristics of these broadband CARS spectra are investigated, and evidence of preferential collisional dephasing and relaxation of different ro-vibrational transitions is not detected. This is a promising but preliminary result to be investigated further in future work.