We use FIRE-2 zoom cosmological simulations of Milky Way size galaxy halos 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 either p-wave (∝ v^2/c^2) or d-wave (∝ v^4/c^4). 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 degrees from the Galactic Center, 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 degrees is more modest and can be higher or lower (∼ 0.3−7). We find these results for s-wave are broadly consistent with the range of assumptions in most indirect detection studies, though our p-wave and d-wave values are significantly enhanced compared to what is commonly adopted. Contrary to past estimates, we suggest that thermal models with p-wave annihilation may be within range of detection in the near future. We then look at the shapes of the emission signal and find that the shape of the predicted J-factor-scaled emission is significantly different in FIRE compared to DMO. Contours of constant J on the sky are well-fit by ellipses. At a fixed fraction of peak J-factor on the sky, DMO runs have short-to-long axis ratios that are typically elliptical at ∼ 0.6, though demonstrate a broad range from 0.4 − 0.95. The FIRE runs are usually rounder, with axis ratios ∼ 0.8, and, importantly have narrower range of expected shapes (∼ 0.7 − 0.85). The long axisis always aligned with the Galactic plane in the FIRE simulations, to within ∼ 5◦. These predictions should be useful as priors in dark matter indirect detection studies, providing new constraints for a detection signal that our high resolution simulations have allowed.