  We present a formalism for estimating the angular power spectrum of
extragalactic gamma-rays produced by dark matter annihilating with any general
velocity-dependent cross section. The relevant density and velocity
distribution of dark matter is modeled as an ensemble of smooth, universal,
rigid, disjoint, spherical halos with distribution and universal properties
constrained by simulation data. We apply this formalism to theories of dark
matter with p-wave annihilation, for which the relative-velocity-weighted
annihilation cross section is \sigma v=a+bv^2. We determine that this
significantly increases the gamma-ray power if b/a >> 10^6. The effect of
p-wave annihilation on the angular power spectrum is very similar for the
sample of particle physics models we explored, suggesting that the important
effect for a given b/a is largely determined by the cosmic dark matter
distribution. If the dark matter relic from strong p-wave theories is thermally
produced, the intensities of annihilation gamma-rays are strongly p-wave
suppressed, making them difficult to observe. If an angular power spectrum
consistent with a strong p-wave were to be observed, it would likely indicate
non-thermal production of dark matter in the early Universe.
