I go with flash for quick get a away or reaching up to the champion to get in range to put ignite on them.
I use ignite to get the final hit on a champion who's about to get away
I use this mostly to scale the jungle and get my red and blue buffs faster but you can replace this because of Udyr's Bear Stance.
This is used to get monsters in the jungle. You should last hit with this to avoid getting buff steals.

I suggest getting this first because Udyr's stances cost low mana but they have low cooldowns so you're gonna spam them a lot. You might run out quickly when chasing someone but with this you have a lower chance of running out of mana.
I use the Hydra for the aoe this is good for when you're low you could use the Turtle Stance to get it back cause the life steal applies to the passive.
The Zephyr would be good cause it has a 10% cooldown and has attack damage which would be good. It also has a 50% attack speed increase.
The black cleaver giver 55 attack damage and it gives 200 health. It also gives 10% cooldown reduction so it gives you 20%
cooldown reduction.
The Spirit Visage helps you get good health and resistance which is good for late game. This gives you 20% cooldown reducion so it's the 40% cap.
this is the final item because it has the lifesteal, attack damage, and an increase of attack speed.

You could use the toggle from the Muramana to get some damage out then Bear Stance to stun them, after that Tiger Stance and claw them. You could Turtle Stance if you want to get the third stack on your passive to get the full attack speed it gives you.

Charge in their with the bear stance go for the highest dealing champion (the ADC). As soon as you stun them tiger them then when the Turtle Stance is ready use that to get your health back then use the active from the Hydra then if they don't die Tiger Stance then keep hitting them. When they die go for the others they probably lost half to a quarter of their health. They might run away or stay.

If they Stay: You probably have Phoenix Stance so use that wait till Udyr breathes fire once. After that use Turtle Stance to get some health back with the Hydra active and passive then tiger, you probably have the third stack on your passive so the Tiger Stance would work well.

If they Run: Bear Stance to catch up to one of them claw them with Tiger Stance if they die do the same thing to the next champion you see.