Here's the review you asked for. I'm just gonna go chronologically through the guide.

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I feel like your Introduction is a tad discouraging. Recommending people to practice lane first is fine but I don't know if you need to explain all the worst possible aspects of jungling right off the bat, haha.

"Did you learn how to kite? If yes, good. If not, you really should learn that. Its your main way of staying alive in the jungle."
This only really applies to certain champions. Plenty of junglers just stand and hit the camp.

"your Brambleback and your xxx"
The blue buff camp is called the Blue Sentinel.

"On red side, you have your Raptors, said Chickens"
I think you mean to say "also known as Chickens."

"there is something known as the Rift Scuttler, read Crab."
Same deal here. Changing to "also called Crab" would be fine.

"and Warwick can clear their jungle with blistering speed"
Warwick's clear is fine but it's not exceptionally fast. Shyvana would be a better example, though her first clear is a bit slower and she speeds up later.

"allowing them to “gank” much earlier"
Might want to explain what "gank" means before you start using the word.

"If your clear is healthy and fast, and the enemy decides to “invade”, and you did your first clear properly, you should be able to fight them off."
This is an oversimplification. Healthy clears help ensure you don't die to invades, but they don't ensure you'll win a duel. Hecarim has zero chance against Warwick or Xin Zhao early game regardless of his pathing. Best case scenario is your teammates collapse on the enemy jungler, but sometimes you just have to back off.

"Along with your proper pathing, kiting, and intelligent use of your abilities, you should also know where the enemy jungler is going, what camps he’s killed, and try and predict where he’ll go next."
This entire paragraph seems out of place. The chapter is about mechanics of your first clear but this is about pathing/counterjungling/jungler-tracking. I'd put this in a different chapter.

"blue -> gromp -> wolves -> chickens -> red"
I would use the official term, "Raptors" rather than Chickens for new players/junglers.

Could maybe add gank routes for red team.

"Another time you’d step into a lane is when your teammate has recalled to buy and the minions are hitting the tower. You should see this and think of 2 things. First, where’s their mid?"
I honestly don't know what their mid has to do with anything.

"Turret aggro increases with each shot"
It would be more accurate to say Turret damage increases with each shot.

"An easy way to do this is by having a sweeper’s lens, which recently became available from level 1."
The item is Oracle Lens.

"Another way to check is to hit the scryer’s bloom, which reveals stealthed enemies and wards."
Scryer's Bloom can give away your position to the enemy team. Be careful about recommending using this for counterjunglers. You can use it to check the enemy jungle, but you should only commit to counterjungling if you know nearby enemy laners won't be able to collapse.

"Basically, punish them for playing the game. If they step onto the rift against you, punish them for it."
I feel like this has nothing to do with what you were just talking about and is kind of meaningless.

"An air drake would help you move faster out of combat."
This isn't wrong per se, but just fyi Cloud Drake gives in-combat movement speed as well now. It's just stronger out of combat.

"One reason is to increase pressure on the enemy. If your team can out-sustain the enemy, you get advantages just from that. The extra mana that a blue buff on your mid could mean more poke onto the enemy."
The point about pressure is true and "more poke" is one benefit of blue buff, but one of the main reasons to give it to your mid laner is to give them a waveclear advantage. If one mid laner can dump their cooldowns on every minion wave and the other can't (because they don't have blue buff), the mid laner with blue is going to have roam priority and likely start gaining a CS lead.

"Next, your ADC and the red is much of the same concept."
I would mention that red buff is typically donated much later into the game compared to blue. Blue provides a major advantage to laners in the early game but red buff is better used on junglers until you start team fighting.

"However, the wards aren’t always used to spot the enemy.

In all honesty, you shouldn’t be using wards to spot the enemy itself."
First sentence is good, second is too far. Spotting enemies is definitely a huge reason to place wards. It's just not their only use.

"If your laners have any degree of competency, they should be doing this on their own, but if you’re reading this, you’re probably bronze. That means you must do the dirty work. If you get the rare knowledgeable teammate, they’ll be doing this work as well. This means that you have wards free to ward other places, like the bushes where the enemy is likely to gank from."
I don't agree with this. The jungler is the freest member of the team and has the most opportunities to place deep wards. Laners most often ward close to the lane or in the river. At best you'll get a ward at the enemy raptors from your mid laner, but that's about it. Junglers shoulder the responsibility to place deep wards in the early game.

"While I tell you to ward the enemy’s jungle, you must keep in mind that you also need to ward the entrances to your own jungle to protect yourself from counterjungling. You also need to ward objectives like dragons and Baron Nashor."
You don't have enough wards to accomplish all of this. Defensive wards can be useful but they should be placed situationally. Tracking the enemy jungler (or roams from the mid laner) and defending your lanes is usually a better use of your wards. You also don't need to place wards directly on baron or dragon early, as those ward spots aren't as useful. The only exception would be if you expect their jungler to try and sneak dragon solo.

"This play is largely centered on the element of surprise and knowing all the participants’ damage."
Baron steals without vision are estimated based on how fast the jungler thinks the enemy team can kill baron. Steals with vision are just 50/50s where both junglers try to Smite at the right time. There's no element of surprise and no player knows exactly how much damage every champion deals during a steal. It's just a judgment call. Maybe in low elo people are surprised by steals but it's really easy to just press Tab and see who on the enemy team is alive and could try to steal. It's also a good idea to have wards up when you start baron so people can't walk up to the pit without being seen.

"When you go in, if you have any crowd control, apply it ASAP onto the enemy jungler so that they don’t have a smite to contest with you."
The only ways to stop an enemy Smite are suppression or knocking the enemy jungler away from the baron. Most CC (stuns, silences, knockups) does not restrict the use of Smite.

"you’ve used your pink ward to remove their vision."
New players aren't going to know what pink wards are. The item name is Control Ward.

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Other than the specific points I've made above, I think your guide could benefit from some more organization and especially visuals. You have a few images with gank routes that are pretty useful. You could add some similar images for red team, since red-side junglers can use different gank routes (like ganking bot through the enemy jungle into tribush). Other chapters with information like tracking the enemy jungler and counterjungling could also benefit from some illustrations.

I say this knowing this is a weakness in my own guides as well. Anything you can do to break up long stretches of text is good for keeping readers engaged, plus visuals can help illustrate a point better than a text description.

It seems like you have a lot of the basics down. My main concern is that the guide is organized according to different concepts, which basically means a new jungler has to read and remember the entire thing in order to apply what they've learned in game. I don't have an easy answer for this, but maybe reorganizing the guide into the different stages of the game could be helpful. Something like Pre-Game -> Early Game -> Mid Game -> Late Game with subheaders for appropriate topics for each section. Alternatively you could cover larger subjects like pathing and ganking in a single chapter and use subheadings to break it up into chunks. For example, "Tower dives" could easily fit in a ganking chapter.

A general jungle guide that covers all the bases and is easily digestible is a pretty tough task. Good luck with your guide. Hopefully some parts of this review prove useful to you. :)