I hope the Flood won't be in Halo Infinite, at least not in a way that's integral to the plot. I don't like the logic plague fan theory that seems so popular right now. And honestly I think the whole "Flood is the true enemy" thing is played out. They had their arc in the original trilogy. Halo 3 was supposed to be the end of the Covenant and The Flood, yet the Covenant limped on for 2 more games and maybe will be in the next one. I don't want the Flood to similarly not have actually been defeated in Halo 3 (something Halo Wars 2 has already kind of done, but thankfully not to the point where the events of Halo 3 were rendered completely useless).
Additionally if we're not on Zeta Halo we could be on the same ring that Anders was on at the end of Halo Wars 2. That came from the Ark, which was shown in Awakening the Nightmare to still have loads of Flood present. Some could have been stowaways.
The Flood had been contained to a single section of the Ark. The containment wasn't broken until after Installation 04c had already departed. Besides, if the new Halo had become contaminated, I doubt the Ark would have sent it on to the Milky Way.