Very good question.
Antinatalism's a dividing line in the anarchist community when it shows up. Not a lot of anarchists hold to the view it's a bad idea to make children. Those that are antinatalist typically range from moderate all the way to really radical.
But if you want to know about a few notable ones who do support it then let me see if I can point out some other notable perspectives some of them have about it.
On the moderate side, the most notable I can think of is an anonymous Greek anarcho-communist. He/she supports antinatalism as a revolutionary tactic to starve the government and weaken it until an anarchist society could be established.
The anarchist introduced this idea in an article written for the Greek branch of Indymedia. You can read the translated version here: http://archives-2001-2012.cmaq.net/fr/node/32288.html
As for the radicals, prominent anarchists who advocate antinatalism and advocate it included, ironically Les U. Knight, the founder of the VHEMT. He's trying to hit two birds with one stone: fight the state and end humanity in favor of helping the planet.
You can read a piece he wrote about his position on the matter here:
Likewise there's an online anarchist blogger named Francois Tremblay. His goal in promoting antinatalism is to make an anarchist society but also to eventually bring about the end of humanity thus ending all suffering.
Here's all the pieces about antinatalism he's got tagged on his blog.
Tremblay's got a huge amount of hate especially from around the internet for being so radical about it. Can't blame his detractors really. His goal in promoting antinatalism is to make an anarchist society to better end humanity.
As for me, I'm an antinatalist that would fall in the moderate category. Pretty much I agree with the previously mentioned article that appeared on Indymedia.
Governments require people to keep having children at a balanced rate to survive. When populations drop, they get very afraid just as they would with overpopulation. In either case, the scenarios are to threat help keep stability and balance thus keeping their machine healthy.
They will do whatever they can to boost birthrates back up to prevent it dying due to a lack of people. Methods they utilize can become very draconian if history teaches us anything. The USSR and the Third Reich were really infamous in their tactics in strong-arming people to have children to raise their birthrates.
So I've employed it myself as a form of refusal in aiding the state and those who depend on people breeding to make more people to exploit. That and it encourages me to work with the people who are already here and trying to get them to embrace anarchism.
Anyway, sorry for the long reply, felt you deserved one given the lack of answers you've been getting so far.
EDIT: For the record I'm a moderate antinatalist. I don't want humanity to go extinct, merely stop having children to starve the beast until we can reach a better world for them to come to. At that point it's safe to say that it'll be fine to make some more within reason.