When you play Shyvana as jungler, you always need to max Burnout, because of the AoE. Shyvanas Burnout is also very good with Red Buff, because you can get fast in at the enemy because of the movement speed from Burnout. Burnout is also very relyable for shyvana because she can farm so fast so her ultimate(Dragon's Descent) will be fast ready again.

Frozen Mallet for shyvana is very good because of her twin bite. When you have frozen mallet you can slow champions and you no longer need the Red Buff to get the slow. She can fast get in on target to slow them, and with Burnout she have no trouble of getting close to the enemy.

This is a very new item in league of legends, this item gives a lot of good stats to shyvana, gives hp and some dmg, which she need very much. This item is also good because when Shyvana gets into a fight she lose a lot of health, this means that this item grants her a lot of dmg, also means that when she is low she is exstremly dangerous. If you buy this item, be sure not to open a fight with your ultimate. try save it for when you have about 50% hp left. It will only make a big surprice that u suddenly do so much dmg. (This item also gives a shield) ;)