I have a longarm and recently quilted minky on 2 baby quilts. They both came out amazing. I spent a lot of time researching and here are my recommendations:
1) Very little to no tension on your rollers or sides. This is so very important. For one of the quilts, I loaded the minky with selvage parallel to my bars. On the other, I loaded the selvage perpendicular to my bars. For both of them I eased up on the tension on my rollers by a couple of clicks and did not use side clamps. No problems with either method.
2) Use a stretch needle and polyester thread.
3) Use a quilting design that is not dense.
Good luck!