The only time I had trouble quilting batiks is when I had a batik backing as well as batiks in the top. Never again! I use muslin backings most of the time.
I used a quilting between, size 11. I would recommend that you use wool or polyester as your batting, or avoid cotton battings like Warm and Natural.
It's usually easier to quilt along the bias, too. It's also easier if you keep the sandwich loose in the hoop or frame.
If you can, try a sample first.
Good luck!
Janet
Edited to add: the quilt in my avatar used Hoffman Tonal solids, very similar to batiks. It's hand quilted, with a Mountain Mist Blue Ribbon cotton batting and a muslin backing. It was a joy to hand quilt.