Hi Emsmom, I live in Washington State just up the road in Olympia and am currently working on rag quilts for my friend's first grandchild. Here is what I do:
Lay out the fabrics the way you like them for the top (I like your idea of using the minki in the corners)
Turn them all over to keep the placement the same (They should now all be showing the wrong side up)
Lay out the fabrics for the back (It is best if you use flannel on one side and cotton on the other front and back so that each "block" is both types of fabric, then mix up the flannel and cotton on both sides of the quilt)
No batting is necessary
Mark your rows 1-whatever you decide (6.5 fabric squares should make about 5x5 blocks so for a 6x7 quilt that would be 14 squares wide by 18 squares long)
Have I lost you yet? You may need more fabric and you would have several options. I like to use chenille, flannel, and cotton in mine but Minki will work just fine mixed in with the other fabrics.
I've been thinking about trying a tutorial but I'm not sure if anyone would use it. Rag quilts are so easy and so cute but they are really messy!
Feel free to PM me (private message) and we can talk off line if you like. Best of luck with your new challenge and have a great time quilting. We would all love to see a picture when it's done.