We don't currently have a way to pack each skin into a separate atlas. We have an issue to track the enhancement:
EsotericSoftware/spine-editor720
You can subscribe to the issue to be notified when the status changes.
If we had that feature, it would only help if you always want one atlas per skin. It would not be sufficient if you want multiple skins in one atlas.
The most flexible solution is to write a script to copy your images into a temporary folder so you can pack them like you want. For example, copy all the images you want in a single atlas to a folder, then pack them. By using a convention to organize your images and then writing a script, this can scale to any number of images.
A similar solution could be to parse the skeleton JSON data to get all the image paths for each skin. Then you can copy them to a folder and pack them. This has the added benefit that you could write application specific logic, like combining multiple skins into a single atlas.