I think there are examples of systems with the same spectrum flatness but different PAPR. If your question concerns a specific area then I do not know the answer.
Spectral flatness characterises an audio spectrum. The spectrum of a system reveals the presence or abscence of certain frequencies while the PAPR (a problem common to OFDM systems) gives a measure of howmuch the signal is into the non-linear region of the Power amplifier and can generare out of bound energy (spectral regrowth) and inband distortion.