I think if this were my quilt, I would back the basket square with something just to keep it on a par with the flannel. Perhaps a piece of muslin or the stabilizer you mentioned.
For quilting, since you wanted to think flower, I would go corner to corner from the center out, skipping the center yellow square. Since there is no batting, you don't have to worry about spacing. So starting at the corner of the center pink square, sew to the middle of the pink square, turn and sew to the center of the next pink square, turn and sew, until you return to the starting point. Then you can backstitch and cut or you can SITD to the corner of the next row, the green, and repeat with each row of the larger squares.
Then for the smaller yellow and white squares in the corners, I would do a fan stitch from the outside corners to the points and corners of the large blocks finishing with SITD or outline stitch around the entire fan.
LOL is that clear as mud? I just could see it in my mind very clearly.