You have to use R very carefully. You can jump in, Zhonyas, Jump another time, run away and port out. Then wait for the Ult CD, hit minions or sth with W to regain mana and head into Battle again. Its possible! Try it!

Without any mana using his R is impossible

Typical comment: You cannot max an ability at level 8

xD I agree on Seraph's Embrace on Kass full-heartedly, but I think this build was made more towards burst and having fun rather than complete legitimacy. Also, I wouldn't use Riftwalk's mana based damage as a way to justify mana ( Seraph's Embrace) on Kass - even with over 2k mana, the added rift damage is still laughable compared to the damage given to his other skills from any other expensive AP-based item. Half the time you won't even be hitting someone with Rift :P. What makes mana important on Kass is simply the stacking mana cost of Rift and the max % restoration from Nether Blade.

Dun b doubtin the Deathfire Grasp on Kass though, cause adding roughly 500 damage and over to Kass's combo is something no other item can do, either!

Finally, I would just put 3 points in either Null Sphere or Force Pulse depending on your situation in lane, since Null Sphere adds to your laning survivability but Force Pulse has AoE and a slow that increases when leveled, making it the better choice after lane (ganks, fights, clearing, etc). The need for stacks on FP is pretty obsolete since they're pretty easy to acquire + FP can affect more than one target when needed, while Null Sphere does nothing for AD's other than damage and has a higher cooldown, too. After those 3 points, I'd prioritize Nether Blade and max that as soon as possible. Its the only thing that justifies Rifting close to an enemy and deals fairly more damage than anything else Kassadin has to offer, especially with Lich Bane. (everyone underestimates Kass + this item...)

Anyways, I think the author's build has more than a sh*t ton of burst and albiet difficult to use, looks pretty fun to try out :D. If anyone's wondering how I knew all of this, I have my own Kassadin guide on this site if anyone's feeling curious and wants to learn more.

Nice work!!! Try to add ways you can cheese people - this build screams that (y). 1+ from me!

Kassadin really wants items like Seraph's Embrace to support his mana heavy early game. He snowballs really well anyways and with mana items he'll also do damage with his ULT and be able to harass opponents for longer.

As for burst, Kassadin has the highest base mana in the game, allowing him to get over 80 AP out of a Seraph's Embrace plus the amazing mana sustain. This is only a little more than Deathfire Grasp but remember it also greatly increases your ultimate damage, something DFG can't passively do.

For your skill order, it's better to max Nether Blade 2nd for the low cooldown burst it offers, as well as the decent mana sustain. Remember that it does the same damage as all of your other basic abilities, and it's utility is always good to have, while the other ones are a lot more specified to match-ups. Generally you'll want to go R-Q-W-E. E last because all we need it for is the CC. We'll usually need the magic damage shield of Null Sphere early on and with the high AP ratio, your E will gain a lot of damage anyways when we begin to buy AP heavy items so there's no need to max it until we have to (again, unless of course you don't need the magic damage shield, in which case you'd go R-E-W-Q for the same reasoning).