Apocalypse World doesn't have a “mechanics are the fictional physics” design — both mechanics and non-mechanics are first-class citizens in the rules, and when the game says something happens, it happens even without being “backed up” by mechanical-looking things. It doesn't matter if it looks like a mechanic or “fluff”, it happens. In AW, game fiction is perfectly fine happening without being underpinned by a mechanical shadow. The game just hums along, stuff happening even when moves aren't being triggered.
Even when looking at moves, we don't need to go find a mechanic to make the move happen. So what's the game say about moves? Well, a lot of stuff on pages 9–11, but this is probably the kernel this question needs to focus on:
All the moves list what should happen on a hit, 7–9 or 10+, so follow them.
So Step into the flow does exactly what it says: any member of the group that is sick or injured is healed. Boom, done. No cross-referencing with the Angel's kit, no searching around for healing mechanics, just do what the move says.
But “How much?”, you might ask. All of it. If they're still injured or sick, you didn't heal them. You healed them, so now they're not sick or injured. This follows the design of the game not putting either mechanics or fiction first, but making them co-equals. See “Prescriptive And Descriptive” in the Improvement chapter for the clearest expression of this (p. 258; emphasis mine):
The players’ character sheets are both prescriptive and descriptive. Prescriptive: changes to the character’s sheet mean changes to the character’s fictional circumstances and capabilities; […]. Descriptive too: when the character’s fictional circumstances or capabilities change naturally, within the character’s fictional world, the player can and should change her character sheet to match.
Totally healed in the fiction? Then erase all those segments of Harm — the sheet is changed to match the fiction.
But, why no looking to the healing mechanics? Because that's not how the game works. Things don't need to be underwritten by mechanics to happen, they can just happen. And “prescriptive and descriptive” is the rule for how to interpret that mechanically, if you have to.
Just like where in most game, you don't need mechanics to say how “yeah, Brenner walks down the stairs without falling on her head” happens, AW doesn't need mechanics to say “yeah, Brenner heals Ambergrease” when the game just said that happens. There are general healing (and getting worse) rules, but you use those when the game says to use those. Step into the flow didn't say to go use them, so you don't. And the Angel's kit isn't the definition of how all healing works, it's just one way someone can intervene for someone's survival.
So is this quicker than going to an Angel? Yeah. You've got the Source, it does that.
Does this mean that a Waterbearer can heal way better than the Angel with nearly no potential consequences? Well, no.
On a miss you open your brain to the psychic maelstrom, and let me tell you, the game gets interesting when that happens. (I was going to write “and you won't like it”, but that's not accurate: even if it's “bad” for your PC, something big happening with the maelstrom can be super fun.) The first time someone opened their brain to the maelstrom on a miss in the last game I played, they learned that the maelstrom was an angry maelstrom, and that they just got its attention. That made every future interaction with the maelstrom suddenly have much higher and much more unknown stakes.
Who knows what your game's maelstrom is going to be like. But when you find out, and when you keep interacting with it, that's not dodging a bullet (well, sometimes it literally is), it's putting your face into the barrel of the cannon and saying “hello?”
But on a hit you're free and clear, right? No opening your brain! Well, no.
You've got the Source, and just healed a whole crowd of people. That's going to have repercussions, good and bad.
You have the Source. That means your life is Complicated already, and probably about to get more Complicated. Moves snowball, and you just pushed a big snowball downhill! This is what makes a AW campaign so involved and so much fun.
An ending note: “This One Common Mistake Will Shock You!”
In my years of playing AW and its children, and talking about them online, over and over again I run into a mistake new players make all the time, and I just want to make sure you're not doing that. I can't tell, but questions like this sometimes (but only sometimes) answer themselves after fixing this mistake.
Read the whole rules. If you've read how moves work and stuff and have figured out equipment, don't stop. You haven't read all the rules yet! You've read maybe 20% of the rules and are missing the whole central engine of the game still.
In most RPGs, the rules for “how the PCs do stuff” is like 99% of the game's rules. In AW, that's super not true. In AW, unlike in most games, the majority of the rules — and all the important ones — are the ones for the MC to follow and the players never use.
If you haven't read, studied, and gone “aha!” while reading The Master of Ceremonies chapter yet, you won't ever really understand the rules the players use. The MC chapter's rules are what glue everything together into a game engine instead of just a collection of moves.
In AW 1e the MC section comes after everything else, and it was really common for people to stop reading before they got to it, because it kinda looks like a complete game up until then, with instructions on how to answer the two questions “how do I make a PC?” and “when I try to X, what do I roll?”, which is, honestly, what most RPGs boil down to.
In AW 2e the MC chapter comes much earlier, right after character creation, so it's harder to miss but hey, RPGs have trained us to skip the “GM section” as being watery advice we don't actually need to read, right? So maybe you've skipped it, or maybe you read it but didn't really turn on the “I'm reading rules” flag and let it kind of float by, like it makes sense to read most RPGs' GM sections.
Anyway, I don't know if you've made this mistake, but if you have, cool! There's a whole weird game engine you're about to discover, and it accomplishes things in a way that most RPG players haven't dreamed possible. It's cool, and I envy you the chance to discover it for the first time.
And if you have read it, that's cool too. I can't tell from your question, because it could honestly still come up after reading the MC's rules. I just wanted to make sure, because wow, so many people I've seen online would have had an easier time learning AW and its children if someone had just gently told them that most of the game's rules are in the MC section.