It's impossible to help just by looking at the video. At a minimum, we'll need the exported Spine files (.skel/.json/.atlas/.png), and ideally a minimal reproduction sample, e.g. a simple .html file that loads and sets up the skeleton by e.g. queuing the animations and setting the skins that have the issue.
Just based on the video, it looks like z-fighting. You can try increasing the SkeletonMesh.zOffset value from 0.1 to something higher. That depends on your scene depth, and what type of depth buffer you are using.
