I love batiks and have been creating quilts with them for 15+ years, no problems with my long arm either. I also love flannel and use it a lot. I use it to back quilts, use it for Piecing tops, ( yes even batiks and flannels in the same quilt top) I’m pretty fearless when it comes to mixing fabrics. I’ve never used a flannel sheet so don’t have any idea if that makes a difference. I use good, double sided ( meaty) flannels most often, like Moda Woolies and Benartex flannels. I also purchase 108” wide flannels for backings from fabric.com- that is probably a lot like a sheet. Just prewash the flannel.