I jungle shen like he was a tanky ap nuker. With the new rebuild boosting his AP as much as possible gives you a ton of health regen for the team, really strong shields and some nice damage output (you will be suprised what you can do).

The tanky part comes in that you choose AP items with MR and Armor attached where you can.

Base your gear selection order after crystal scepter on the enemy team and how fed / good each player is.

You are a tank, not a damage dealer, but you can damage deal and you cant tank constantly.

Aka. Dip into a fight, deal some damage, taunt some people, throw and ult, leave, repeat.

I take these runes for insane energy regen on the new shen and it just makes your damage output significantly higher.

Pretty standard Jungle masteries + some nice ap damage increase.

I almost always get merc treads and crystal scepter. Anti CC + a slow on your throw/taunt makes sense + a nice HP boost.

Then I base my item order on the enemy team and how good I feel there damage dealers are. If I consider them to have better AD damage than AP I go straight into a frozen haert, if the AP is stronger I get the abysal scepter first. Then I get the other item right after.

At this point the game usually ends but if it hasnt then stack more ap/vamp heal for team + a towerdive taunt followed by zhonyas can change a team fights outcome.

Smite - obvious
Flash - just my preference, I like to taunt in then flash out of big teams, drags them in my direction and I dont get destroyed instantly, or for ganking flash > taunt is good from bushes.

Alternatives

Ghost - pretty good just like flash
Ignite - not that helpful but meh damage none the less
Exhaust - good in a team fight focus it on carries
Heal - not really needed but if no one on your team has it maybe

Do not take
Revive - unless your super pro and die once/twice a game
CV - let the support do that
Promote - just no ...

Jungle route - Blue - Wolves - Wraiths - Red - gank a lane - wraits - wolves - gank - repeat. I usually ignore golem unless I am going past them, just takes too long and is to far out of the game.

For general jungle gameplay I always use 1 hp pot + spamming vorpal blade on the blue buff.

Wolves I use a 2nd hp pot + vorpal & shield to recover to almost full hp.
Wraiths I just vorpal & shield then for red I have 1 hp pot left vorpal & shield. After that do what you feel.

In a team fight generally Shield > taunt > vorpal > retreat > repeat. Ult if you have to on your carry/ap's .

The goal for jungle shen is to bully lanes around with your taunt vorpals and shield. If you see a player dying ult on to them or if you see a player winning encourage them to tower dive and ult them to take the initial damage of a tower / other players.

Try and get enemies out of lanes, returning or spending ults & summoner spells, if you can get a kill then brilliant even better.

Try to be everywhere at once(atleast mentally), if your jungling watch your champs as much as you can so you can see opportunities to gank with your ult or save a player.

Whilst you have DPS gear its main use is for your shields and heal factor, do not chase a single target 1v1 unless you are 110% you will win.

You are a tank, but dont hang around for the whole of a fight, dip in and out with taunts and shield and just keep kiting people on you away from the team or taunting the whole team of your carry etc.

In summary, bully everyone, never die, dart in and out of combat with your shield and taunts, vorbal the main target for team heals + damage and dont be afraid to ult.