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We use FIRE-2 zoom cosmological simulations of Milky Way size Galaxy haloes to calculate astrophysical J-factors for dark matter annihilation and indirect detection studies. In addition to velocity-independent (s-wave) annihilation cross-sections 〈σv〉, we also calculate effective J-factors for velocity-dependent models, where the annihilation cross-section is either p-wave (∝ v2/c2) or d-wave (∝ v4/c4). We use 12 pairs of simulations, each run with dark matter-only (DMO) physics and FIRE-2 physics. We observe FIRE runs produce central dark matter velocity dispersions that are systematically larger than in DMO runs by factors of ∼2.5–4. They also have a larger range of central (∼400 pc) dark matter densities than the DMO runs (ρFIRE/ρDMO ≃ 0.5–3) owing to the competing effects of baryonic contraction and feedback. At 3 deg from the Galactic Centre, FIRE J-factors are 3–60 (p-wave) and 10–500 (d-wave) times higher than in the DMO runs. The change in s-wave signal at 3 deg is more modest and can be higher or lower (∼0.3–7), though the shape of the emission profile is flatter (less peaked towards the Galactic Centre) and more circular on the sky in FIRE runs. Our results for s-wave are broadly consistent with the range of assumptions in most indirect detection studies. We observe p-wave J-factors that are significantly enhanced compared to most past estimates. We find that thermal models with p-wave annihilation may be within range of detection in the near future.