It's important to distinguish between the BLM network, co-founded by Patrisse Khan-Cullors, Alicia Garza, and Opal Tometi, and the BLM movement, which is a far less well-defined collection of anti-racism groups and individuals. The New Yorker describes the latter as "eschewing hierarchy and centralized leadership".
The BLM movement has a very loose organizational structure. According to the BLM network website, there are currently 16 BLM chapters, 13 in the USA and 3 in Canada, however, clearly this is not the whole story as BLM protests and activists have present all over the world. These chapters are subject to some sort of central regulation, although the quote below gives a different figure for the number of chapters.
There are now more than thirty Black Lives Matter chapters in the
United States, and one in Toronto. They vary in structure and
emphasis, and operate with a great deal of latitude, particularly when
it comes to choosing what “actions” to stage. But prospective chapters
must submit to a rigorous assessment, by a coördinator, of the kinds
of activism that members have previously engaged in, and they must
commit to the organization’s guiding principles. These are laid out in
a thirteen-point statement written by the women and Darnell Moore,
which calls for, in part, an ideal of unapologetic blackness. “In
affirming that black lives matter, we need not qualify our position,”
the statement reads.
In an interview with InTheseTimes, Garza summed up the membership & organizational structure of BLM, and how the network relates to the movement:
Folks use BLM because it gives them a platform. At the Black Lives
Matter Network, we aren’t concerned with policing who is and who isn’t
part of the movement. If someone says they are part of the BLM
movement, that’s true—if they’re working to make sure that Black lives
do matter. But we don’t control the movement.
This sentiment was echoed by Cullors in an interview with USA Today:
What sets Black Lives Matter apart from other social justice groups,
however, is its decentralized approach and reliance almost solely on
local, rather than national, leadership. Cullors said organizing is
often spontaneous and not directed by one person or group of people.
“We don’t get (people) onto the streets, they get themselves onto the
street,” she said.
To give an illustrative example; the recent 15,000 strong protests in Nashville were organized by 6 girls aged 14-16 on Twitter.
As far as funding is concerned, this is also hard to pin down, as it comes both in the form of donations directly to the BLM network, as well as to the network of anti-racism groups that contribute to the movement as a whole. For example, the Washington Times reported in 2016 that the movement was "increasingly awash in cash, raking in pledges of more than $100 million from liberal foundations", these being the Ford Foundation, Borealis Philanthropy, George Soros' Open Society Foundations, and the Center for American Progress. Note that these donations didn't go directly towards the BLM network, but instead to funding vehicles such as the Black-Led Movement Fund.
Politico reported in 2015 that "some of the biggest donors on the left" in the Democracy Alliance were being lobbied to help fund the movement, again through decentralized groups rather than the BLM network:
The DA, as the club is known in Democratic circles, is recommending
its donors step up check writing to a handful of endorsed groups that
have supported the Black Lives Matter movement. And the club and some
of its members also are considering ways to funnel support directly to
scrappier local groups that have utilized confrontational tactics to
inject their grievances into the political debate.
Some of the groups mentioned are Black Youth Project 100, The Center for Popular Democracy and the Black Civic Engagement Fund.