Hi slawek,
here is a file i did fast and because of that things are not perfect but should show how it can be done.
on the first layer is how it works. check the vertex groups for body and skin wings. also check the cloth sim.
on the scond layer is a model. when you model that bat in this pose it is much better for animation and rigging in my experience.
third layer shows some better topology for the skin between the fingers(just click the model then you see some crease pencil notations.
this is how i would do it… good luck!
edit: did something wrong with vertexweights of the body that causes stretching of the fingers. here is a file where it is fixed: