The only way I will quilt fleece is with a good quality basting spray.
Spread the fleece, with the good side down, spray the fleece, then spread the pieced top evenly over the fleece. When using fleece, you really don't need any batting. But if you do, choose a very thin batting. I don't like spraying the basting spray on the pieced top because it might soak through.
I also, after quilting, trim the the fleece two inches wider than the top all the way around. Then I pull it over the top and hem it all around. Gives a nice edge and is very sturdy.