Welcome!
You can mix all types of fabrics. Cotton and flannel - absolutely. Cotton and shiny may be a bit trickier.
Don't be afraid to cut into it. You say you've got enough fabric now. This weekend is as good a time to start as any!
I guess my first suggestion is to see if you can cut a nice straight 2" strip. If you need more practice, you won't have wasted too much fabric.