How do they explain Brianna's american accent?

I was wondering about that too. I guess she could have said she came from the American Colonies, which is what I would have expected her to have as a back story.

First off, there is no single "British accent." They tend to be regional, much like in America. A few years ago I had a shot at doing some voice-over work for a founding fathers project. I had assumed that they would have had British accents. As it turns out, some of the accents in England were far less pronounced than they are now, some sounding very close to an American accent today.

"How do they explain Brianna's american accent?"

uh , what?
whose they?
'they' explain it by her being american.

e.g.
"Why miss Breanna, what is that accent you have"
"I grew up in Boston, thats in the new world dont you know .."

job done.

Brianna already has a British accent. Some time between the 1700s and the present, the British changed their dialect. Tecnically, the British should sound "American" and Claire's dialect should sound odd to everyone. Also, some words and grammar should be different in that time period.

In the colonies, people are used to hearing all kinds of accents and not knowing where they originated. Laoghaire did mention that she did not recognize her accent, so she must not be from around there.

Seems like people notice her accent is different, but they aren't particularly concerned about it. She keeps telling people that she's from Boston, but I'm not sure there's anyone on the show (other than Claire, Roger, Bree) who's ever been to Boston. So it's really a non-issue.

If I recall, someone said "you're a newlander", implying she came from North America.

I’ve also read the books, so I might confuse them with the show, but I could have sworn that Claire said several times that her daughter grew up in Boston in the new colonies...