I think I'd use very thin batting (since it would be two layers) and an almost cheesecloth type material to hold it in place.
I've got a Brother machine, but it's handled my fleece and flannel rag quilts well, and I've mended blue jeans on it well before.
it will end up looking like a window, hence clouds, and then I'm appliqueing on the front window sills and a cat looking out the window, and then on both layers a sun and sunbeams...
so that from the front, it looks like you're looking outside, but from the back, it would almost look like you were outside just seeing the sun.