Flat or inverted nipples should make no difference, ask my mum, she didn't get me totally off the boob 'til I was almost 3 and they're still flat as pancakes!! But she was a midwife and then a health visitor so she knew the technique.
What might be required is a different latch and lots of support. Also, bear in mind that it takes time for the milk to come in and your milk supply is related to demand (so as baby demands more your body produces more, with a delay of about 24 hours or so). This means that when baby has a grown spurt (every six weeks or so) he or she may feed a lot and seem not to be getting enough milk. Keep feeding and it will be fine, your milk supply will catch up.
Your local NCT should help (you don't have to join, they will help for free). Your MW should have the times and locations of local breastfeeding support groups (there's one 4 days out 5 in the 3 villages surrounding me). I've also heard La Leche is very good.
Like riding a bike or a horse, it's a skill that takes time to learn. Don't panic, no baby ever starved in the meaintime and it is normal for them to lose a bit of weight in the first week or so.
Sorry if any of the above seems patronising, I don't mean it that way and realise it isn't your first. It's just that I've spoken to a number of mum's and their reasons for giving up seem to be more about not understanding the process than that there was anything actually wrong. A lot of mums also don't get enough support, although there's a lot out there now you do have to reach out for it, I think.
I hope that helps.