The biggest strength and greatest failing of the False Emporer's Imperium is that it's armies are so vast that they treat war like a game of chess. wear down the opponent by simply overwhelming him and killing everyone. as long as you win, no one cares how many of your people died in the process.
Were i the Leader of a Black Crusade, I would spend centuries, Milennia even, planning my glorious march and collecting resources. Start by claiming Systems the Imperium doesnt know/care about. between hereteks, Daemonic inspiration, and traitor rogue trader and navigator houses (they're out there) it would be very easy to carve out Warp lanes to star systems that hold riches and knowledge the imperium doesnt have. In this sense, you create a kind of Anti-Imperium (or true Imperium, whatever strikes your fancy), from which you can properly launch attacks and regroup when you need to. Then you take the time to seed one and only one entire segmentum with sleeper agents and well disguised servants to destabilize the Imperium's hold on that area. after sufficiant destabilization and corruption of the segmentum to make it open to the idea of change (i.e chaos) You attack the imperium with a traditional Black Crusade (mass invasions of Imperial planets, rending of Warp Barriers to let in daemons and such, and the like), staging this incursion at an area that the imperium nowhere near the segmentum you seeded with traitors. As someone already pointed out, The Imperiums apparently infinite armies and limitless resources will eventually stamp out this crusade, but make is so large that it will take a while. then, take your true Black crusade to Annex the Segmentum you seeded. you now control a major portion of the imperium. then you repeat.