I love combo in cube but ultimately find that regularly cubing with a cube that supports storm combo is pretty painful since so many of the storm cards are awful outside of the deck. Other combos, like Grindstone/Painter's Servant or Time Vault/Untapper are either too narrow, too-few pieced, or composed of actual awful cards.
Essentially what the combo is trying to do is either copy a creature that has an untap or blink ability with Kiki-Jiki, Mirror Breaker or Splinter Twin. Kiki-Jiki/Splinter Twin combo is one of the better and keeps the amount of "bad" cards you have to play to a minimum. (The latter needs an untap ability.) The best part is that these "bad" cards aren't straight-up unplayable like Brainfreeze or Tendrils of Agony is outside of a storm deck. These are the cards that I think are necessary for the deck:
Kiki-Jiki/Splinter Twin: The namesakes of the combo, they are the cards that do the blinking over and over. The latter doesn't work with something that would instantly blink the creature, since the Splinter Twin would fall off, but works with most of the cubeable creatures that keep the combo going. These cards can be bad outside of the combo deck, but cube cards still often have ETB abilities so they can work in decks that gain you a lot of value off your creatures. Personally I like having both in the cube if you're going to run the combo because you want to give the combo as much playable redundancy as you can, and I think both cards are baseline fine even if Splinter Twin is decently worse.
Pestermite/Deceiver Exarch: I think both of these, like Kiki and Splinter, are necessary for the redundancy of the combo, though both are definitely the worst cards outside of this deck. Pestermite is at least a 2/1 flier with flash, so he can fit in any aggressive/tempo blue build, and tapping or untapping a thing can always be useful out of either creature. More often than not they'll make a sideboard when the combo is not fully supported, but Exarch is a great sideboard option versus an aggressive deck and a flier with evasion is fine even in cube. Also these cards will wheel for the combo deck, allowing them to shore up their deck in the early packs where either 'mite or exarch is seen and the drafter can take a better blue or red card.
Imperial Recruiter: While not necessary to the combo, I only like Recruiter when the combo is around, though I can understand if it's played without the combo supported as well. Recruiter is great because it grabs you both Kiki Jike or either the Pestermite or Exarch, acting as a utility tutor that you can copy again if you're trying to find other answers like a Glen Elendra Archmage or Ghitu Slinger. Outside of the combo he's good in decks where he can grab a lot of different creatures, though I think he's at his best in cubes where the Kiki Jiki combo exists. The card is expensive, but if you proxy (don't ask how) or have one/are willing to invest, it's worth adding to support the combo.
Restoration Angel/Zealous Conscripts: Both of these work with the combo (Restoration Angel only works with Kiki Jiki) but I feel are good enough to run without the combo and would be a mistake to marry them to the archetype of the kiki/splinter combo. Wizards printed both of these cards after the combo was known to exist, showing that they are willing to support the deck at least in modern and eternal formats. The archetype should only grow stronger over time.
I also like the kiki/splinter combo because not only is it pretty fair and not the hardest to interact with, but once you set it up and launch it the game ends much quicker than most other combos do where you need to set up ridiculous amounts of plays before you can even use all the mana or storm count you accumulated. If you have no interest in running the Exarch/Pestermite/underwhelming card package, I could see this not being for you and that's completely understandable, but I feel that the combo is strong enough to support with the few spots it needs.
I play all of my Kiki combo pieces on their own merits. The fact that they combo together is just gravy.
First off, with Restoration Angel and Zealous Conscripts, I don't think anyone has to defend their inclusion.
For Pestermite, I support blue tempo/devotion, so I've found the card to fit quite well. I'll admit it is a bit of a pet card and a tad fringey, but I'd argue its performance I've seen in the tempo decks has warranted its inclusion.
Lastly, Kiki-Jiki is just a fun iconic card. People in my group see the card and want to try and draft the deck for it. The weird interactions and fun gamestates it creates every time it lands, plus the 'build-around-me' nature of its ability + cards like Sneak Attack helps to carve it's own archetype out of my red section.
For the others, I don't run Imperial Recruiter because $$$$$$$$ and while Splinter Twin is a cool card I think it's too vulnerable to run for straight value.
I love combo in cube but ultimately find that regularly cubing with a cube that supports storm combo is pretty painful since so many of the storm cards are awful outside of the deck. Other combos, like Grindstone/Painter's Servant or Time Vault/Untapper are either too narrow, too-few pieced, or composed of actual awful cards.
Essentially what the combo is trying to do is either copy a creature that has an untap or blink ability with Kiki-Jiki, Mirror Breaker or Splinter Twin. Kiki-Jiki/Splinter Twin combo is one of the better and keeps the amount of "bad" cards you have to play to a minimum. (The latter needs an untap ability.) The best part is that these "bad" cards aren't straight-up unplayable like Brainfreeze or Tendrils of Agony is outside of a storm deck. These are the cards that I think are necessary for the deck:
Kiki-Jiki/Splinter Twin: The namesakes of the combo, they are the cards that do the blinking over and over. The latter doesn't work with something that would instantly blink the creature, since the Splinter Twin would fall off, but works with most of the cubeable creatures that keep the combo going. These cards can be bad outside of the combo deck, but cube cards still often have ETB abilities so they can work in decks that gain you a lot of value off your creatures. Personally I like having both in the cube if you're going to run the combo because you want to give the combo as much playable redundancy as you can, and I think both cards are baseline fine even if Splinter Twin is decently worse.
Pestermite/Deceiver Exarch: I think both of these, like Kiki and Splinter, are necessary for the redundancy of the combo, though both are definitely the worst cards outside of this deck. Pestermite is at least a 2/1 flier with flash, so he can fit in any aggressive/tempo blue build, and tapping or untapping a thing can always be useful out of either creature. More often than not they'll make a sideboard when the combo is not fully supported, but Exarch is a great sideboard option versus an aggressive deck and a flier with evasion is fine even in cube. Also these cards will wheel for the combo deck, allowing them to shore up their deck in the early packs where either 'mite or exarch is seen and the drafter can take a better blue or red card.
Imperial Recruiter: While not necessary to the combo, I only like Recruiter when the combo is around, though I can understand if it's played without the combo supported as well. Recruiter is great because it grabs you both Kiki Jike or either the Pestermite or Exarch, acting as a utility tutor that you can copy again if you're trying to find other answers like a Glen Elendra Archmage or Ghitu Slinger. Outside of the combo he's good in decks where he can grab a lot of different creatures, though I think he's at his best in cubes where the Kiki Jiki combo exists. The card is expensive, but if you proxy (don't ask how) or have one/are willing to invest, it's worth adding to support the combo.
Restoration Angel/Zealous Conscripts: Both of these work with the combo (Restoration Angel only works with Kiki Jiki) but I feel are good enough to run without the combo and would be a mistake to marry them to the archetype of the kiki/splinter combo. Wizards printed both of these cards after the combo was known to exist, showing that they are willing to support the deck at least in modern and eternal formats. The archetype should only grow stronger over time.
I also like the kiki/splinter combo because not only is it pretty fair and not the hardest to interact with, but once you set it up and launch it the game ends much quicker than most other combos do where you need to set up ridiculous amounts of plays before you can even use all the mana or storm count you accumulated. If you have no interest in running the Exarch/Pestermite/underwhelming card package, I could see this not being for you and that's completely understandable, but I feel that the combo is strong enough to support with the few spots it needs.
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First off, with Restoration Angel and Zealous Conscripts, I don't think anyone has to defend their inclusion.
For Pestermite, I support blue tempo/devotion, so I've found the card to fit quite well. I'll admit it is a bit of a pet card and a tad fringey, but I'd argue its performance I've seen in the tempo decks has warranted its inclusion.
Lastly, Kiki-Jiki is just a fun iconic card. People in my group see the card and want to try and draft the deck for it. The weird interactions and fun gamestates it creates every time it lands, plus the 'build-around-me' nature of its ability + cards like Sneak Attack helps to carve it's own archetype out of my red section.
For the others, I don't run Imperial Recruiter because $$$$$$$$ and while Splinter Twin is a cool card I think it's too vulnerable to run for straight value.
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My 630 Card Powered Cube
My Article - "Cube Design Philosophy"
My Article - "Mana Short: A study in limited resource management."
My 50th Set (P)review - Discusses my top 20 Cube cards from OTJ!