Stretch. That's the big problem with fleece. The first time I tried fleece on my quilt frame, it was a disaster. I had to remove every stitch and start over. The problem? I didn't load the backing with the selvage on the sides, but instead at the top and the bottom. And it stretched, very badly stretched. Fleece like most fabrics stretches the most on the width of the fabric. It's much more stable along the length. Loading the fabric on the frame (even cotton) with the length of the fabric running up and down instead of side to side will minimize stretch and subsequent puckering.
Loading the fabric properly helps but doesn't solve all the problems. There's still that side to side stretch - lots of it. Originally I was using the clamps that came with my frame on the sides but this posed lots of problems. They hung down so that when I was using rulers and the ruler base, it hit against those big clamps. They also were so heavy that they stretched the fleece. Fleece stretches very easily on the width of the fabric so it requires more care than quilting cotton. Somewhere on the internet I saw a solution that I liked. No idea whose video I was watching so I can't give credit. Here's my version - not real pretty but they work great. (That's a scrap of cotton batting there on the right that I use as a thread catcher - important as I have a cat who loves to eat thread and I'm tired of vet bills)
I took two fabric scraps (one for each side), hemmed and added a casing for the dowel. I cut a couple of slots where I could wrap the Velcro around the dowel. The fabric is pinned to the backing on the side, then the Velcro straps are stretched and attached to the frame. The dowel keeps the tension consistent as does pinning end to end (I typically use 4 large pearl head pins). Pinning takes a little longer but honestly it's easier on my wrists than those clamps. The fabric and dowel are thin and light so they don't pull the fabric down and they don't get in the way when using rulers. I can quilt to within an inch of the edge with no problems. With the fleece, I only put just enough tension so that the Velcro straps don't sag. But no more. This keeps the fleece flat but doesn't stretch it. Don't pull taut like you would with quilting cotton. This is very important if you don't want ugly bubbles along the edges of the quilt.
One other trick I've started using. My machine is only 16" but my frame can accommodate a larger machine (maybe someday). I had a hard time remembering where I needed to stop as I was quilting. Nothing more frustrating thinking you have room to do one more swirl and ending up with a flattened donut instead. I thought why not put a guide to give me a warning when I was getting close. At first I used the leader from the bar meant for the quilt top (I float my quilts), but then one day I got too close and sewed through it. Hmm, how about a ribbon. I baste each side of the border as far as the machine will reach, then use that as a guide to pin the ribbon. This gives me a visual cue as to have far I can go before I get into trouble. I've only caught the ribbon once and I just cut it instead of my stitching.
One more thing. I float all my tops, meaning I don't use the bar on my frame meant for the quilt top. I've found that the fleece holds the top smooth and flat enough that I don't need any tension and it makes loading the quilt faster and easier (not my favorite part of frame quilting). I leave the bar on the machine and the canvas leader provides a little bit of tension as does the weight of the top hanging down. As I get near the bottom of the quilt I will pin the top to the backing when I can see it's needed to keep things flat and even. I've started floating tops like this even when using batting and cotton backing. It is so much easier to smooth out the batting as I go when the top is hanging loose. I guess if you are doing heirloom or dense quilting it might cause problems but so far I've not seen any need to roll the top on the bar. Sometimes I have to chase the cat away as he thinks the quilt hanging down is a toy but then he thinks everything is a toy. For large quilts and quilts with batting, I made a type of sling or hammock from slippery lining fabric to keep things off the floor (but that cat thinks that's a really fun hammock -sorry, no pic).
In case you were wondering, the red strips in the picture above are called Red Snappers, a system of plastic grips used to attach the backing to the canvas leaders. They are very quick to use but they take some getting used to. Initially I had some problems using them with fleece but over time they've loosened up. I've also gotten the hang of flexing them as I press down but you do need a flat solid surface to do it. Removing the leaders from the bar helps. I attach the top of the backing to the back bar first and roll the entire thing loosely onto that bar. Then I attach the bottom leader, making sure it's 90 degrees to the edge of the fabric. I carefully attach the leader back on the bar, making sure it's straight, not shifted and the fabric is 90 degrees to the bar, then I roll everything back onto the bottom bar slow and even. As mentioned above I can get an entire bolt rolled this way unless it's especially thick fleece.
Thanks for reading, hopefully some of the things I learned the hard way (my favorite way to learn) will be helpful and save others some frustration.