I had one flat nipple and one 'normal' one and found it very difficult to feed from the flat one.
Things that helped were:
Gently but firmly pushing back around the flat nipple when engorged, to sort of push the milk pressure back and create some space to make a cone to push into babies mouth.
Breast shells (not shields) that are worn between feeds. I think these had the same effect as above, as the edges of the cut out hole pushed back around my nipple. Added bonus was that my nipples also didn't have to touch anything between feeds.
Lansinoh nipple cream. Slather it on at every opportunity and use breast shells to stop it ring wiped off onto bra/pad.
Use a pump to draw out the nipple. Be careful not to pump too hard though, as you don't want to cause even more trauma to your nipples
Play with it 
. White lots of Lansinoh, tiny late the nipple lots so that it is as erect as possible as often as possible. Sort of gets it used to being 'out there' 
When it got very sore to feed from the flat side, I pumped and fed from the other side. At or point I fed both my twins from the none flat side, pumping from the flat side at every feed for a whole week! Gave my flat nipple a chance to recover, but took my other boob to stupendous proportions (was lopsided for most of the first year as a result). The effect would probably be much less pronounced if you don't feed two babies from one side for so long.
It is hard work and painful at times in the early weeks. It is sometimes difficult to reconcile ourselves with this reality in the face of lovely soft-focus mum-and-babe breastfeeding images, but it really can be quite a difficult skill to master.
Remember that every feed is great for your body, your babies development, and gets you one feed closer to the ease that is established breastfeeding :)
^^