Great questions, glad you found us here
I have spent time matching up backing fabric patterns. It is worth it if you like it and you have enough fabric! A lot of people don't care... but I am one who does. On the other hand, I'm not such a fan of flannel. I have pets and dust allergies and am all to aware of that especially on dark flannel...
I personally think regular woven fabric on the binding is fine. I've done donation quilts with flannel on the back, and a matching flannel binding against a regular fabric top. The flannel is thick and reacts a bit when used as binding. There are different grades of flannel, the lower cost flannels can be skimpier thread counts than the "quilting" level, I'd be concerned how well a low cost flannel will last at the corners -- but then again, I don't use flannel enough to know. Fortunately, other quilters here do use flannel enough.
You do have to watch the shrinkage warnings for flannel as well. Even if you didn't prewash the front fabric, you might want to consider washing and drying the back on high heat. You might be able to find a 2 yard x 60" wide flannel wide enough for your project, that makes it pretty close to your 53" measurement. But how are you going to put the quilt together? Machine quilt? Hand tie? Quilt by check (done by someone else) each quilter has requirements.