We have the same problem, severe flat nipple. We tried many method, but found the use the breast pump to be the most effective. Use the pump to slowly suck out the nipple. The initial few days it may be painful but after a few weeks the nipple will be more willing to come out and stay for a longer time when you use the pump. We found nipple shield or the Philips niplette not as effective and may cause abrasion.
Then come 2 options, to pump awhile then let baby latch or to just collect into the bottle and feed. We chose the latter as it's easier to gauge the volume and less stress to both mom and baby. And the baby is not denied from the nutrients from the mom's milk.