This is my first guide on here, but I've been using this build for quite a while. Bear with me if this talking section isn't exactly up to par.
What this guide is designed to do is get you so you can hop in on team fights, take damage while dealing your Katarina's ultimate, but stay alive because of the amount of health and spell vamp she gets from her Will of the Ancients. I have not yet been able to play ranked, but as soon I can, I will make edits to this if they seem like they need to be added.

The reason for choosing the Flash/Ignite combo is because you can use flash to escape being ganked in conjuction with ShunPo to a minion, preventing a pretty terrifying gank if you are in mid lane. You can also use it to surprise enemies at the distance you can cover with just these two abilities. Ignite is something that you can use with your ult on someone who is just not dying fast enough for you to be happy with. extremely useful when losing a foe to one of their turrets.

Farming is essential to any character, but the great thing about katarina and part of the reason you want to max out bouncing blades first is because you can use the strings of minions to hit otherwise out of reach champions. Bouncing them off of minions in a straght line to a champion is a great way to harass the other one in mid and keep them off your case. This is also a very useful way to pick at a foe's health until you can shunpo in and snag the kill before they have a chance to react/you have time to escape the turret.

Using this build, I have been able to carry my team, while not being an AD heavy set up. Death lotus is best when used 1v1 or in the middle of a team fight since a team will sometimes have a hard time focusing the character stealing all their health with 4 other champs attacking them.

There are quite a few pros, and a couple cons to this build that I would like to explain.
First of all, the cons. Because of the way this build is set up, if you run into too many people or the wrong person in the jungle or on the way to a teamfight, you are probably dead because, other than health and spell vamp, you're not build for armor.

The biggest plus side to this build is the fact that because you have a lot of health by the end of it and so much spell vamp, returning to base will almost never have to happen as long as you can keep up the harassment on the enemies or keep getting minion kills with your spells. Also, chances are, unless the other team built a lot of magic resist, you will probably not have a problem running around ganking and taking out single targets.