In the movie Avengers: Infinity War, Dr. Strange saw 14,000,605 futures; in Loki, Kang and the TVA coordinate just one Sacred Timeline.
Then were the other 14,000,604 futures terminated by the TVA? Did Dr. Strange see that future and know about Kang and the TVA?
Q: In the movie Avengers: Infinity War, Dr. Strange saw 14,000,605 futures; in Loki, Kang and the TVA coordinate just one Sacred Timeline.
This is a statement, rather than a question, but it's important to address this, as it appears that your subsequent questions are based at least partly on a misconception about the Sacred Timeline.
As I explained in this answer, the writers of Loki didn't do a very good job of outlining what the Sacred Timeline is (or was) within the series itself, but when you factor in statements made by the writers in various interviews, the implication is that the Sacred Timeline isn't truly a single timeline, but rather a bundle of similar timelines, which share the same broad history, but differ on some of the finer details (like whether Loki is male or female, black or white, etc).
It's also the case that He Who Remains and the TVA never truly erased the rest of the multiverse. They just isolated the Sacred Timeline from the wider multiverse, and kept pruning its branches to keep it isolated. When He Who Remains was killed in Loki S01E06, that pruning apparently stopped, and new branches from the Sacred Timeline began to grow freely, eventually reconnecting it with the wider multiverse.
The relevant evidence for all this is cited in the linked answer.
Q: Then were the other 14,000,604 futures terminated by the TVA?
Strange said that he used the Time Stone to view 14,000,605 alternate futures.
STRANGE: (Speaking breathlessly) I went forward in time to view alternate futures. To see all the possible outcomes of the coming conflict.
QUILL: How many did you see?
STRANGE: 14,000,605.
TONY: How many did we win?
(Strange pauses a while before answering)
STRANGE: One.
Avengers: Infinity War (2018)
The implication is that he was merely looking at alternate futures, not creating them. It's unclear whether he was seeing alternate timelines that actually existed somewhere in the multiverse, or whether the Time Stone was just showing him projections of how the conflict with Thanos could unfold. Either way, there's no suggestion that new branching timelines were literally being brought into existence.
Also, it was made clear in Loki that whenever a new branching timeline began to form, the TVA had to act quickly in real-time in order to prune it, before it grew past a red line depicted on their instruments. If they took too long, and allowed a timeline to cross the red line, pruning it was no longer an option. The exact time limit wasn't specified, but based on what was shown, it was implied to be a matter of minutes, not hours, days, or years.
MISS MINUTES: Okay, y'all, let's review what we've learned. What happens when a nexus event branches past red line?
LOKI: Very bad things.
MISS MINUTES: Come on, Loki. What is it?
LOKI: ( Sighs ) It's when the TVA can no longer reset a nexus event. Okay? Boring.
MISS MINUTES: Right. And that would lead to the destruction of the timeline and the collapse of reality as we know it.
[...]
LOKI: Let me ask you this, why don't we just travel back to before the attack, when the Variant first arrives?
MOBIUS: Nexus events destabilize the time flow. This branch is still changing and growing, so you gotta show up in real time.
Loki - S01E02 - "The Variant"
In the first five episodes of Loki, and the beginning of episode 6, the Sacred Timeline is depicted as a single, roughly horizontal stream, which suggests that Strange didn't create any permanent branching timelines in Avengers: Infinity War.
Loki - S01E06 - "For All Time. Always."
It's also quite hard to believe that the TVA could've acted quickly enough to prune over 14 million new branches within a matter of minutes. Their staff wasn't obviously presented as being that vast in number.
Even if we theorise that the TVA did successfully prune over 14 million new branches in a matter of minutes, it'd mean that none of those new branches extended more than a few minutes beyond their respective nexus events.
Which begs the question: how much could Strange realistically have learned by viewing such short-lived branches? And the likely answer is: probably not very much of practical use. Realistically, he'd need to view possible futures that weren't being cut short by the TVA's pruning activities, in order to determine how the various permutations of the conflict with Thanos actually concluded.
Q: Did Dr. Strange see that future and know about Kang and the TVA?
It's unlikely that Strange learned of the TVA's existence. As I explained above, I don't believe he was viewing timelines that were ultimately pruned by the TVA.
And even if we theorise that he did see some TVA Hunters and Minutemen showing up on Earth to prune timelines, it's by no means a given that he'd therefore know about He Who Remains as well.
With the exception of Miss Minutes, most or all of the TVA staff didn't know about He Who Remains; they thought their bosses were the Time-Keepers. Loki and Sylvie only learned of his existence by travelling to the Citadel at the End of Time, which was presented as being a very mysterious and difficult place to reach.
So, just seeing some Hunters and Minutemen wouldn't be enough, in and of itself, to inform Strange of the existence of He Who Remains. He'd need to do a whole lot more digging to uncover the truth behind the TVA, and there's absolutely no reason to believe he did any such digging, or that he saw any Hunters or Minutemen in the first place.
As the good Doctor admits in Spider-Man: No Way Home, he knows very little about the multiverse, so it’s not unreasonable to assume that his Time Stone activities in Infinity War might not be creating the sorts of branches that the TVA concerns itself with.
And as he says in Infinity War, he’s looking into possible futures. There’s no indication he’s actually creating them, in the way that Loki somehow is when he steals the Space Stone and tries to conquer Mongolia by standing on a fairly small rock. (Neither Loki nor What If…? actually explain how branches in timelines or universes or whatever are created.) So presumably there’s nothing for the TVA to pay attention to.
And as we learn at the end of Loki, the TVA aren’t actually trying to prevent all timeline branches: just ones that will lead to another variant of He Who Remains imposing his will on the multiverse, instead of the one that we meet. The idea of one single, so-called sacred, timeline may just be part of the TVA’s mythology, there to give its staff a glorious purpose to fulfil.
