I'm sure some people will disapprove of what I'm saying, but it worked for me, okay, so please don't have a go at me, I'm jsut trying to pass help along.
I too have flattish nipples, and quite large breasts which early on swelled up like melons. My son had slight tongue tie which all contributed to a major latch-on struggle. As the lactation consulatant put it 'he's trying to suck a pimple off a football!'. She recommended a nipple shield. This goes on over the nipple and has 3 or 4 small holes in it which the milk can pass through. It worked BEAUTIFULLY. After a couple of weeks my engorgement reduced and I was able to feed without the shield, but then a couple of weeks later DS seemed to find his strength and started pinching really hard, hurting a lot when he fed. I went back tot he shields and again the problem went away. We're back without them now.
Some people may tell you this will lead to nipple confusion. Since you say you're already giving EBM (our of a bottle, I presume!) and breastfeeding, I doubt one more nipple shape will matter.
Might be worth a try for you.
Best of luck,
Cath