I love to start with flask and 3 pots because of the survivability it gives you. Furthermore you have the sustain to handle any strong AP burst with this starting item. However if you are versus an AD bruiser i would personally start with red pot for a nice all-in and again survivability vs ignite.
Nothing else to say here except that if you get first-blood rush tier for faster stacks even though you complete it at 4th - 5th item its strong for early mana all-ins

Pros for Kha'Zix :

Strong early burst
Leap away from ganks
Nice lifesteal from W
Very fast in moving around (including leap)

Cons for Kha'Zix :

Squishy early game
Can be caught out with stun very easily
Can miss time his W and mess up completely with timing

If you have any more ideas please comment below

Brutalizer : Very good for snowball since it gives you 25 AD , 10% cdr (cool down reduction) and 10 armor pen , which stacks nicely with your runes and masteries (roughly 22 armor pen in total after you get brutalizer)

Tier of Goddess : I'd say its needed on all mana burst champions who can put out a lot of damage in combos , however due to the lack of mana in early levels the champions (e.g kha'zix) fall out because they run out of mana. Therefore this item is a must on kha'zix unless you feel you aren't going to be spamming spells so much

Boots : It completely depends on what you are facing against , mostly you should buy Mercs or Mobility, but it all depends if you are vs CC or not. For example if you are against a team with slows i would go for anti-tenancy shoes so that you have the chance to go in quicker. Whereas if the team lacks CC or you know its a hard one to land (e.g skill-shot) then I would take mobility boots so that you have the ability to move around very fast (great for roaming).

Bloodthirstier : Everyone needs this on Kha'Zix , even though it is a silly item since Kha relies on spells not AAs , you are purely building AD so its a good item to have vs meele champs if your spells are on cooldown , not much to say about this item because it is overall great for all sorts of AD carries aswell. Although you obviously dont have any spells that proc the lifesteal , you have your evolved ultimate which resets your unseen threat which is quite nice to use if you want to spam AAs down real quick

Last Whisper : A must have on all AD champions , especially if enemy team is stacking armor , it will shred through very quickly, it also works well with masteries (43% armor penetration in total + 22 from items if you go for the build I choose) but yes it is a must have on all AD champions even for spells since they do physical damage

Omen : Extremely helpful in both situations; running away and chasing down. First it is good to escape with because you can pop the Omen right on top of the enemy and then leap away ( if that is not enough you should pop your ultimate ). Secondly it is good to chase down because of the movement speed reduction it gives (I think 20% or something like that) it is also strong vs kiting enemies because it reduces their Att speed and Movement speed at the same time whenever they cast an AA

When :
Only all in if you are confident that you can burst the champion down , be sure to harass first if they have some source of shields , barrier etc then go for a last final blow onto them pop your ignite and run away (it is not safe to tower dive after ignite is ticking away because they could have a stun e.g TF and could turn things around)

When not to :
Like listed above never go all in vs people with cc as you will be dramatically behind in DPS and they could initially burst you down. A clever thing to do is if you are below 200 health and they are full hp they will probably be cocky and dive you ( works well with barrier ) so when they try diving you let them hit the cc (slow , stun etc) but then quickly leap away as far as you can pop your barrier , or ignite them and kill should be secured

Kill yaaamp kill yamp kill yamp :DD

OCELOTEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Like a boss yumping around

Never should you ever build items that proc with AA (other than BT) because as we all know kha zix is a champion which is a bruiser relying on spells , therefore i would also not take him vs a team who has 2+ silences as you can be dramatically shut down
Guardian angle : Even though you might be fed dont get so cocky in late game and underestimate the enemy damage I've seen many people go in 1v3 lose their GA , die , and lose the game
Spread the kills : Yes its nice to get fed but like above , if you get so cocky and dive in they will just focus you and pick of the rest of your team so try to spread the kills around and if a lane is behind ask them to roam around and give them a kill so they can get back in their lane
Evolution : Never ever evolve ****py Q it is pointless +50 range in Q +20% dmg and +50 AA range which is almost nothing to be honest , first evolve W then E to yump around then ulti for great escapes

Thanks for reading my guide ! :)