It depends. If you end up with enough hens for the Delaware and large enough hens for the Brahma, you'd be okay, IF they eventually work out the alpha male thing and get along with each other. I don't have hatchery Delawares but my heritage Delaware male could keep up to 25 hens fertile and he'd never accept another male in his group-I tried numerous times. He actually killed one of his sons once when that male was about 25 weeks old and surpassing his sire in size.
Delawares are active breeders. Brahmas are usually quite large and can hurt smaller hens. So, you really would need more hens, IMO, to house those two together with one group of hens. The Delaware needs at least 10-15 of his own hens, though if you kept only the six, you could see how it goes with JUST the one male.
Not sure how prolific a breeder a Brahma is, but he's super large, so he needs BIG hens. Most hatchery stock in those breeds you mentioned are not very large. He'd be okay with his own breed but the Australorps and hatchery Dels are not very large.
You don't have enough hens for those two males, JMHO.
ETA: I asked a moderator to move this thread to the management section for you.