Debbie,
I'd buy new flannel for this project and prewash it. Then use the flannel that you've already cut for another project. Prewash it in a lingerie bag. My sister uses the lingerie bag for her small fabric pieces and she reports that it cuts way down on the fraying.
If new flannel isn't an option then follow Ruth's suggestion and add a border. But do prewash before using it. Flannel is notorious for shrinking a lot.