What sort of equalization I need to apply to my headphones when listening to audio that is binauralized using my Aural ID?

You have two choices. One is the on-head equalization of the headphones for completely flat response in the ear and the use of the Full HRTF Aural ID (provided). The other is the standard high quality diffuse field equalized headphones and the use of the DTF version of the Aural ID (provided). The second is fully personalized but not as accurate the use of Full HRTF. You will experience small sound colour and direction uncertainties. The reason for this is that the diffuse field equalization models the CTF in the HRTF but it is an average over several persons and not your personal CTF. Headphone manufacturers also have their own wide band sound colour emphasis, for example the bass level varies a lot between different headphone makes.