Why am I not getting a flat phase for a Gaussian pulse when doing a Fourier transform in Python?
The group delay will be flat assuming the filter is linear phase (which means the phase is linear vs frequency). Group delay is the derivative of phase with respect to frequency. Either unwrap your phase and detrend it or use the group delay function that is part of scipy.signal to evaluate directly. Any FIR filter (not just the Gaussian) will be linear phase if (and only if) the filter coefficients are symmetric or anti-symmetric.