Hi, Clément-
I'm a little confused about what you are after here.
The affine file contains parameters for global translation, rotation, shear and scaling. The WARP file contains the local displacements that get applied voxel-by-voxel.
If you want the full warp from your input dset to the template space, you want to combine *_composite_linear_to_template.1D and *_shft_WARP.nii.gz. This is what is input into afni_proc.py in most situations, as described in the help.
For the Jacobean, you certainly *don't* want the global translation and rotation included (those are the rigid body parts of the transform). I guess the question is do you want the global shear and scaling from the affine, as well as the local displacements from the WARP, or just local displacements themselves?
--pt