At the beginning of the game try to collect Regen Globes as much as possible cause this will increase your mana pool a lot and will help for your 16 level talent ( )thus this will prevent you from dying alot when assasins come to gank you.
Please have in mind that with this build you wont have the sustain to put a lot of AOE damage in the team fights, however u will be able to nuke squishies for about 2 seconds if everything goes well. I will explain now your positioning in team fights and how to deal the burst of 2200+ damage for 1 second so u can even nuke Raynor without having him to activate his 'E' ability.
1st comes protection... always consider your allies picks for example to use this build in order to win u have to be protected by a warrior and a good sustain healer cause ur going to be the most squishy there yet ull be doing the most damage and this makes u the worst threat to the enemy team and they will have to eleminate you.
2nd is positioning... With this build u dont have to apply chain bombs to the target so its easy for you to take it from the back lines, if they come to gank you from behind consider using your E ability and activate your (have in mind that this is your only self protection from assassins so use it properly and carefully)
3rd NUKING... the biggest part of the nuking will happen after you hit level 13 and take the Flamethrower talent however i will explain how to nuke for example Raynor for 1 second :D.
At level 20 when u have already picked up your Arcane Power talent (this nuke works even without this talent but probably wont nuke him in most cases when he has Uther or Kharazim for support cause they can neutralize the burst) pick up on a squishy target and cast your then wait for a little while before the impact and when u see the gigantic ball of fire is about to hit its target cast immediately while u are still under effect for the extra 15% ability power (almost no assassin can survive this burst exept The Butcher cause he is way too giftet with life.

Play Video
Here's also a video how i do it. Arthas has 5220 HP at lvl 20 and i bursted 60% of his life for about a second.

At level 1 i pick because of the mana pool it gives me late game to support (in some case when u are playing a Quick Match instead of Hero League and you are not having a support consider picking because it helps your health sustain a lot while laning against someone who can poke you endlessly.. its a good option.

Level 4 i mostly pick it gives you this nice feeling of stacking ability power when u bring someone down and its best used with ability damage dealers like yourself. If u are not confident enough that you re not going to hit the target facing you with consider picking . About .. it is also an option but i wont recommend it since the nerf.

Level 7 the only option i would recommend here is cause it is the only talent at the current level which boosts your damage.

Level 10 is personally my favorite ability of KT and i have developed a nice build to go with it so i would recommend not picking while using this build order.

Level 13 picking is a must!.

Level 16 is a must also in most scenario cases but if u are confident enough in your protection u can also try or consider what do u need more Protection, Damage or extra CC.

Level 20 is little bit tricky. is not very popular talent in most cases but i pick it anyways so i can sync the ability power from and also boost my ability damage output in team fights yet gain some mana if i am low. If u are not confident in your teammate's protecting you (trust is hard gained in SOLO Q i've also experienced it :) ) is always an option.
Thank you in advance for hearing out my guide for Kael Thas and i apologize for making any mistakes altho this is my first guide so far hope u like it and have fun in solo Q with it :)