Hi Guard, this brings back memories! We had pretty much the same situation with dd. I think some babies just do sick and posset - certainly dd did, which was a shock after ds, who could wear the same babygrow for days without a mark on it.
I wonder whether you need a face-to-face session with a Breast Feeding Counsellor, perhaps a change in positioning will help.
Certainly your dd sounds windy. Have you tried drinking fennel tea yourself, as well as giving her a couple of teaspoonsful a day?
It's possible that she is a sucky baby, and what seems like a long feed is actually her trying to satisfy the desire/need to suck. Go ahead and give her the dummy if you see that it helps.
In the early weeks/months, it seemed to me that dd would get very frustrated at the lack of instant milk before the let-down, suckle intensely for a while, then get very frustrated again at the slow trickle after she had 'emptied' the breast. She fed a little more peacefully if I gave her the dummy to suck for a minute in my arms before the feed, then whipped dummy out and boob in.
Do you try winding her in different positions? If the burp doesn't come up easily, try changing her nappy and then burping her again. You can do bicycling exercises with her legs, and bunny hops, while she lies on her back, to try and help out bottom burps. Possibly not after a feed if she's a sicky sort, but at other times!
This may all just be her settling down, and you'll just have to keep going until it eases. I believe that breastfed babies develop their gut fauna faster than bottlefed babies, and this can lead to them having a lot of distressing wind.
HTH