Small guide on how to play Jungle Taliyah
https://image.prntscr.com/image/G1DZ4b2uQtywHuuMAycSZg.png
I really like jungle Taliyah, because just like Ezreal, I think it fits her thematic better. It's also very fun to play and sometimes the reactions of the enemies when they get stomped by a Taliyah jungle is really funny.
Runes used: https://image.prntscr.com/image/0iw1gDoYTxu73ZchqAxK6w.png Masteries used: https://image.prntscr.com/image/dwMcB09jS_64zGLFMHEcLA.png
Build: https://image.prntscr.com/image/xmuxIi7CRA2byGIcJuOHdA.png
Notice: I usually go CDR boots instead, but decided to build tabi cuz the entire enemy team were AD. Last item either
or 
I Always start at Blue buff, because I need the mana especially in early game.
My jungle order is usually Blue > Wolves > Raptors > that crab in the river > red buff I do that order, because I use smite either at blue or on wolves depending on the leash I get and I definitely need smite for red, so I kill the crab to get health back, kill time for smite to recharge and grant vision in the river for my bot or toplane.
After getting red buff I usually try to counter gank, because I finish red at the time most enemy junglers are about to gank, so I will be there to assist my laner and often get a kill out of it.
Afterwards I clear jungle camps whenever I see them to reach level 6 to get the ultimate gank power.
How I gank:
When teammates are alive https://www.youtube.com/watch?v=FTYz9ynearM&feature=youtu.be
When teammates got killed https://www.youtube.com/watch?v=QUtS-AkjeV8&feature=youtu.be
Taliyah works quite fine in jungle if you know how to play her, but is not and probably will never really be meta. Little tip: when doing the first raptor camp, use your trinket to ward your red buff, it happened a few times to me that the enemy jungler waited at my red to cheese me. Despite being played as the jungle role, she is still a mage and that means she is squishy. Be aware of your positioning and never try to fight enemies alone. She is - after all - a teamplay based champ.
Disclaimer: Do NOT try this in ranked before you played it 10 - 20 times in normal games with great success.

being the one I hate most. But yeah, she is not the best jungler, but she is one of the most fun ones.