If I understand your plan, you are going to lay the front (made into 12 blocks) and the back rights sides together, stitch around the edges leaving an opening, then turn. You do plan to stitch around the outside edges, closing the opening used for turning, and then stitch around ALL the blocks on the front of the quilt? If you do that and stitch around all the blocks through both the flannel and the fleece on the back your quilt will be fine. If you don't stitch the fleece back to the front in some areas, the back will separate from the front when washed. Be aware that you will need to be careful that the fleece on the back doesn't shift or creep as you stitch and you end up with folds and/or tucks in the backing. Try pinning the two together before you start and be sure to use a walking foot. It can be done as I did it with just fleece and flannel to make a snuggle quilt for myself when I first started quilting. I just did channel stitching at about 5 inch spacing across both the width and length.
Good luck. Sounds like a really snuggly quilt.

You could tie the quilt. Donna Jordan Fabrics recently did a wonderful video on this method.

My experience putting two pieces of fleece together (sewed together) is they stick together and don’t bag. Not crazy about fleece but that's What my grandson wanted.

After you birth the quilt I suggest you smooth it out, make sure the front and back line up and then pin it and stitch a few lines about 8-10" apart horizontally through all layers. This will keep the front and back layers from shifting. Just make sure to smooth to out so you don't have puckers. Then I would top stitch the edges, I'd do the edges last because when you sew the lines horizontally it's possible the fabric will stretch. So if you top stitch it first you will have a big pucker at the sides.

You should machine quilt thru both layers to hold it in place. It is a baby quilt so it will get a bit of abuse and a lot of washing - make it secure! Also, after you turn it (pillowcase style), press it and pin it a lot. The easiest quilting for a newbie is to do a diagonal line down the center and work out to one corner, flip around and work out to the other corner. This allows for the least amount of fabric in the harp of your machine. Make sure and only stitch a bit, move your hands, then stitch a bit more. This will help you not get puckers underneath. For the 'binding ' edge, stitch in about 1 1/2" to give the look of a blanket binding and avoid the extra bulk of the fleece seam. With each quilt you make, you will learn the tricks and each will be better. You will also learn how to do more intricate quilting and finishes. - practice makes better. You are making a treasure - enjoy!

I agree with what others have said about the back needing to be attached to the top here and there in order for it not to billow out separately. Because fleece is very stable, you don't have to do a whole lot of quilting. It could be tied, but I find that more tedious than machine quilting. You could just stitch a bit every 6-10 inches in every direction, perhaps a bubble or loop and then travel to the next one in a wide arc.. If the baby is a girl, maybe a free-motion flower here and there. They're fun to do. Watch some youtube videos. It's important to make a swatch of the type of fabric you plan to use, and test/practice. Also, the flannel should be washed first because it will shrink much more than the fleece.

Top stitching around the edge of a birthed quilt is a good idea, but not sufficient to keep it neatly together. Just picture a toddler dragging it by the middle of the top layer, and you'll be able to see why.

Welcome to the board from Arkansas.

Another suggestion is to make a self-binding baby blanket using the pieced top as the top. There is a tutorial at the MSQC website. Here is the link https://youtu.be/lqwdNqMZ8Ro The dimensions would be bigger than what is shown, but if you then stitch around the blocks after you get the binding, it would be really interesting.

Our group makes a lot of baby and wheelchair quilts with either cotton or flannel as the top and fleece on the back. Both layers are quilted (stitch in ditch; decorative) about every 6-8" apart. Some fold the fleece over to make a self-binding and machine stitch; others stitch around the outside edges and use a scallop blade in their rotary cutter on the edge instead of binding.