A higher order spectral analysis of the OH time series from a turbulent jet flame (75% H2/25% N2) is first presented with the purpose of studying the phase coupling and asymmetric shapes in turbulent flames. The bispectrum and bicoherence, which are a measure of non-linear phase coupling between three quadratic frequencies, have been calculated for time series in turbulent flames with varying Reynolds numbers and spatial positions. The experimental time series were obtained using picosecond time-resolved laser-induced fluorescence (PITLIF) in both jet and counterflow geometries. Noise was found to have an insignificant effect on the trend of phase coupling. A “triple correlation”, which was found to be characteristic of asymmetries in the time series, was compared with the bicoherence, and was found to correlate with the total bicoherence. The strength of quadratic phase coupling in the jet flames increases with Reynolds number. Fundamentally different structures in the spectrum were found for different relative positions in the flames. For the present time series the real part of the normalized bispectrum carries the major characteristic of the bicoherence, while the imaginary part of the normalized bispectrum is randomly distributed.