Tahm Kench is a decent jungler for one simple reason.
Tahm Kench can win any early 1v1.

TK is a champion with little combat mobility and very poor against multiple targets, but when it's about staying and fighting he's the best there is.

Pros:

• The BEST duelist
• Good diving potential, both when tanking and to shift aggro with devour
• Natural tank
• Ultimate is a low CD mid-range teleport, excellent for ganks
• High CC, strong skill-set

Cons:

• Bad against multiple targets
• Bad against heavy CC
• Bad against %hp
• Devour/Ult requires some skill

8.23
Customization of rune stats - 1-10% CDR is very strong as it frees CDR from items

ghost is a must to keep up with enemies. It's strong in ganks.

Tahm Kench's passive. Solid damage bonus that increases with stacks up to triple. At maximum level it provides 5.25% hp/hit which is very strong.
Tahm Kench's relies on this passive to empower his offensive spells so stacking it is very important.

Skillshot with good range. Procs a strong slow which is useful for engaging and a stun when empowered which is extremely important in fights. Very similar, but unlike Blazing Stampede it doesn't have an internal cooldown for the same target so Tahm Kench can re-stun as often as his CD allows, up to every 3s with 40% CDR.

One of the strongest skills in the game and a very hard one to use since it can do more harm than good.
Defensively it can be used to deny damage and combos against teammates.
Offensively, since it's dealt as a suppress and it lasts up to 4 seconds it can deny a lot of enemy abilities and effects.

• Deny almost every form of CC on an allied champion (but careful with AOE effects as it will disable TK as well)
• Deny grabs such as Death Sentence and Bone Skewer
• Cancel Ace in the Hole
• Deny Hextech Ultimatum
• Devour while getting hit by Keeper's Verdict to carry Poppy to your base.
• Gets rid of annoying pets such as Daisy! and Summon: Tibbers
• Douches Jarvan's dash mid-flight with Dragon Strike
• Outlasts Kayle's Intervention, Kindred's Lamb's Respite and most of Tryndamere's Undying Rage.
• Can be used against Master Yi both to wait his Highlander out and to cancel Meditate
• Can cancel any dash mid-air, but it's hard timing.
  
  Additionally:
• Wait out Exhaust from an ally
• Remove suppression (damage still applies)
• Cancels turret shots
• Can spit enemies into friendly abilities such as Yordle Snap Trap and Event Horizon
• There's often enough time to ping and call for a friendly skillshot to hit an enemy as it's being regurgitated.
  
  It must be noted that ongoing damage effects continue to apply on allies devoured so it won't protect from bleed, Ignite and Death Mark.
  
  Devour does a lot of %maxhp damage which is great for finishing enemies off. regurgitate applies a 0.25s stun so a good combo is Tongue Lash+stun -> Devour+wait for CD -> regurgitate+ Tongue Lash+basic attack.
  
  Finally, Devour can be cast for free while Tongue Lash is mid-air to grab a minion or monster. This isn't very good in duo lane because Devour cooldown is too long to waste with poke, but it's good to grab cannon minions and very strong at stealing monsters. Tahm Kench can easily steal the rift Herald.
  
  Devour is a suppression so Tenacity doesn't apply and it's only broken by suppression breaking effects such as Quicksilver Sash.
  
  
  Thick Skin is an one-point-wonder that's responsible for Tahm Kench's being so hard to kill. Good for holding tower aggro.
  TK is very vulnerable without this skill. Avoid activating it too early.
  This passive benefits from Spirit Visage.
  
  
  Very powerful and often underrated skill. It's similar to Destiny but has a far shorted cooldown, can transport an ally and can be used much more liberally in the mid-game as Tahm Kench can do much more than Twisted Fate when in a bad position.
  
  It's main use is to support plays. At level 1 it's range isn't very good, but with good map vision and positioning TK can be ready to jump in for a gank, invade or counter-gank.
  Tahm Kench can give very serious ganks in top-lane, but also can gank bot-lane as well.
  Thresh and Bard are considered good for ganking, but they are nothing in comparison to 2 players falling right behind an over-extended lane.
  
  Abyssal Voyage is also good to get faster to a lane or objective and also for split-pushing with the proper items.

Domination

Hail of Blades procs TK's passive 3 times for damage and enabling quick stun and devour. Hail of Blades is extremely strong for Tahm Kench. He's a great duelist and this rune makes him overbearing, especially in the early game when he can 1v1 most champions and even when underleveled.

Taste of Blood is somewhat decent early. There aren't good options after Cheap Shot nerf.

Good to have some extra map visibility. Zombie Ward is good but doesn't do much before you swap trinkets.

Relentless Hunter provides a lot of easy out-of-combat ms which is very important for roaming and backing up the whole team. Tahm Kench is very slow and this helps a lot.

Inspiration

Approach Velocity provides a lot of mobility and is easily one of the strongest runes for Tahm Kench. Against enemies TK can now use Tongue Lash to slow and get a 15% speed bonus to close the distance and then quickly attack with Hail of Blades to set a stun or Devour. Also provides 15% speed to reach CC'ed teammates for easier Devour.

Magical Footwear gives delayed free boots. Tahm Kench doesn't need to rush boots anyway since the other mobility runes will cover him. The extra +10 movement really helps TK later as he is very easy to kite.

TK has a poor clear before Bami's Cinder, but strong duel. Prioritize fighting for Heralds and easy blue-side camps.

Start preferably bot-side,do buff and Gromp then fight for Herald. Priority is to kill the enemy jungler, but if the enemy lanes are coming before yours it's possible to QW the Herald then smite.

If your starting side is east/red don't go for Krugs/Raptors because TK doesn't have a good clear. Instead try invading the enemy Gromp for a fight.

Don't power jungle. TK clear is really poor without Bami's, but his ganks are nice when he has ghost and chilling smite.

Prioritize ganking lanes with little mobility or without summoner spells.
Ghost is extremely strong against vulnerable lanes.

Once lvl6 it's easy to gank or counter-gank. Try to time it so TK cuts off the escape route.

TK's dueling is simply stacking the passive and chaining CC.

Hail of Blades allows for quick stacking so hold on using Tongue Lash if the enemy isn't fleeing so it's up to get a quick stun.
Keep attacking and stunning while saving Devour for when the enemy is low. Devour lasts for 4s so when in a 1v1 it's usually best to wait for Tongue Lash out of cooldown to chain an extra Q.

Avoid using Devour too early because the passive is unavailable on CD. Don't panic.