Fleece can absolutely be used as batting. I love to use the really thin fleece sold at Walmart for batting inside baby quilts. It makes the quilt incredibly lightweight and easy for a little one to drag around.
I have a long arm frame to quilt on, so that makes it easier to use fleece. One thing that I will suggest when using fleece as batting or backing is to quilt/sew from selvage to selvage. That is usually the least stretchy, and gives me better results.
I have used double knit as backing, but not as batting. I don't see why it wouldn't work.