Not really, but that could be because it’s a small-ish round cushion and it is pretty stuffed, not much empty room.

I suspect it would be the same for a pillow, if the case is really stuffed, it shouldn’t flatten because the kapok has nowhere to go.

I have a kapok meditation cushion and I find it more comfortable than any other style. I’ve used it as a pillow as well for naps and it is comfortable.

Can’t speak to the allergy aspect, but I think that is probably more related to the cover than the insides.