You should be fine soaking them in your kitchen sink. I would fill the sink with hot-to-the-touch water, then add the flannel and stir really well with a wooden spoon or spatula. Let the water cool down and remove the fabric. Repeat if you think it's necessary. You could then roll in a towel to get most of the moisture out and hang to dry in your bathroom.
By the way, I think you have chosen the perfect pattern for those fabrics.