Does your mod contain the Spine Runtimes? If it doesn't, then you do not need a Spine license to distribute it (though I wonder how you would modify the Spine animations without using Spine). The data files created with Spine are the IP (intellectual property) of whoever created them. However, the Spine Runtimes which load and render Spine animations are our IP and the intention of our licensing is that the Spine Runtimes are only used by Spine licensees.
If your mod contains the Spine Runtimes (including indirectly, eg if it contains Darkest Dungeon which contains the Spine Runtimes) then the Spine Runtimes License Agreement applies:
Spine Runtimes License Agreement
As described there (in legalese), there are two options:
1) If you license Spine, Section 2 of the Spine Editor License Agreement applies which grants you more lenient rights for distribution/etc:
Spine Editor License Agreement: s2
2) Otherwise, you can still distribute your mod containing the Spine Runtimes but will need to make it clear that anyone who uses your mod needs their own Spine license.
Note in both these cases the Spine Runtimes License Agreement needs to be included with the mod.