Crota's fortress and the Vault of Glass exist out of time. They are just themselves. Let's start with VoG.
The vex are no problem, exept Templar. He's the mind of them. Mindless, the flood will never get to him. And without the mind, even infecting the vex will do nothing as the Templar would just re-convert them or destroy them. Even if the vex fail it sacrificing themselves, the oracles would destroy them. The oracles are not machines, or organisms, they are pure nothingness that decides what stays and what doesn't. The flood keeps coming in just to keep getting destroyed. Eventually their ranks are nothing. They can only live outside of the vault.
Say they get past the Templar by slipping through the cracks under his nose, the Gorgons will find them. They aren't smart enough to not try to destroy them.
The flood could consume the vault by infecting the Gorgons. But the Templar will always survive. Awakening the throne is no problem for the flood, neither is Atheon. But they wouldn't make it that far anyway.
Now Crota. Pit? No problem. And all the thralls would make for an army of flood. Bridge might be harder. Who knows, really. Can the flood activate the bridge and get s sword across? Up to chance. Crota, though is an issue. One spore dies, Oversoul. Everything dead. Done. Again, they keep coming in to get destroyed. The flood will eventually run out. Darkness wins. Fallen and cabal are totally -blam!-ed, though.
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If a flood infection form controls a vex then they're entire race is under control of the flood. For the hive, crota, really? You can't be serious! The infection forms would infect him in an instant. And btw, they could just crawl down the pit where the bridge is and climb back up to the other side. Then infect all the hive there, and attack all the other hive. Then with boomers under they're control, they shoot crota and infect him. The end!