Titan Comics, the company you might know from their involvement in the official Dark Souls comics and novels, recently announced that they will be tackling Dawn of War 3 as well. This isn't their first foray into Warhammer 40k, however, given that they currently have an ongoing series called Warhammer 40,000: Will of Iron, the first part of which you can read for free by heading over here.
As for Dawn of War 3, it will be getting a four issue comic mini-series in April 2017, focusing primarily on fleshing out the overarching lore and some of the characters you'll be killing meeting. The comics are being written by Ryan O'Sullivan (who penned the Eisenhorn: Xenos one-off comic, and the Turncoat series), and illustrated by Daniel Indro (who did artwork for Vikings: Uprising and a couple of Doctor Who series). Whether their work is actually any good, that I don't know, but what I can tell you is that some of the Dark Souls comics ended up being pretty solid, so my hopes are high for Dawn of War 3.
If you can't be bothered to wait until April and would like to learn a little bit more about Dawn of War 3, and Warhammer 40k general, you're in luck as Relic has just recently posted a brief lore video. You can find it by heading over here, but do bear in mind that its aimed at complete beginners, so if you're as fanatical about Warhammer 40k lore as I am, you might just find it to be a tad too boring.
And if it is gameplay that you seek, you'll find the recently posted Ork gameplay footage over here. It won't tell you much about Dawn of War 3 given that its just a showcase of how awesome Orks are, but if you're a fan of bullets and tons of flashing colors, it might just be up your alley! Enjoy!