Activate Chromatic Orrery's first ability by tapping it, adding {5}.
Cast Kiri-Onna by paying {5}.
When Kiri-Onna enters the battlefield, it and Mana Echoes trigger.
Resolve the Mana Echoes trigger, adding at least {C}{C}{C}{C}{C}.
Resolve the Kiri-Onna trigger, returning it to your hand from the battlefield.
Repeat from step 2.
If you control five Spirits except Kiri-Onna, this combo will net infinite mana.

Infinite card draw

Infinite draw triggers

Infinite colored mana

Infinite colorless mana

Infinite creature ETB

Infinite creature LTB

Infinite storm count

Mana Echoes

Kiri-Onna

Chromatic Orrery

Cast Kiri-Onna by paying {4}{U}.
Volo triggers, creating a copy of the Kiri-Onna spell.
The Kiri-Onna copy enters, triggering itself.
Holding priority, activate Food Chain by exiling the Kiri-Onna token, adding {U}{U}{U}{U}{U}{U} that can only be spent on creature spells.
Kiri-Onna enters the battlefield, returning itself to your hand.
Repeat.

Infinite colored mana that can only be spent to cast creature spells

Return any number of creatures to their owners' hands

Volo, Guide to Monsters

Food Chain

Cast Kiri-Onna by paying {5}.
When Kiri-Onna enters the battlefield, it and Mana Echoes trigger.
Resolve the Mana Echoes trigger, adding at least {C}{C}{C}{C}{C}.
Resolve the Kiri-Onna trigger, returning it to your hand from the battlefield.
Repeat.
If you control five Spirits except Kiri-Onna, this combo will net infinite mana.

Mycosynth Lattice

Cast Petals of Insight by discarding Kiri-Onna.
Conspiracy Theorist triggers, exiling Kiri-Onna and allowing you to cast it from exile this turn.
Resolve Petals of Insight, putting the top three cards of your library on the bottom of your library, and returning Petals of Insight to your hand.
Cast Kiri-Onna from exile by discarding Petals of Insight.
Conspiracy Theorist triggers, exiling Petals of Insight and allowing you to cast it from exile this turn.
Kiri-Onna enters the battlefield, returning itself from the battlefield to your hand.
Cast Petals of Insight from exile by discarding Kiri-Onna.
Repeat from step 2.

Infinite magecraft triggers

Infinite self-discard triggers

Dream Halls

Conspiracy Theorist

Petals of Insight

Cast Ugin's Conjurant, choosing to have X=4, but paying {0} due to Ezzaroot Channeler.
Petalmane Baku and Kiri-Onna trigger.
Resolve the Petalmane Baku trigger, putting a ki counter on it.
Resolve the Kiri-Onna trigger, returning it to your hand from the battlefield.
Cast Kiri-Onna by paying {U} due to Ezzaroot Channeler.
Petalmane Baku triggers, putting a ki counter on it.
When Kiri-Onna enters the battlefield, it triggers, returning Ugin's Conjurant to your hand from the battlefield.
Repeat steps 1 through 4 one additional time.
Activate Petalmane Baku by paying {1} and removing three ki counters from it, adding {U}{U}{U}.
Repeat steps 5 through 8 one additional time.
Repeat steps 5 through 7 one additional time.
Activate Petalmane Baku by paying {1} and removing three ki counters from it, adding {U}{U}{U}.
Repeat from step 1.

Petalmane Baku

Ugin's Conjurant

Ezzaroot Channeler

Cast Ugin's Conjurant, choosing to have X=2, but paying {0} due to Ezzaroot Channeler.
Bounteous Kirin and Kiri-Onna trigger.
Resolve the Bounteous Kirin trigger, causing you to gain two life.
Resolve the Kiri-Onna trigger, returning it to your hand from the battlefield.
Cast Kiri-Onna by paying two life due to Ezzaroot Channeler and Defiler of Dreams.
Defiler of Dreams triggers, causing you to draw a card.
When Kiri-Onna enters the battlefield, it triggers, returning Ugin's Conjurant to your hand from the battlefield.
Repeat.
Once you have drawn your library, you may cast Ugin's Conjurant with X equaling the amount of life you gained this turn to have it enter the battlefield with a large amount of +1/+1 counters, and to gain that much life due to Bounteous Kirin.

Near-infinite +1/+1 counters on a creature

Near-infinite lifegain

Near-infinite lifegain triggers

Bounteous Kirin

Defiler of Dreams

Cast Kiri-Onna by paying {U}.
Radagast and Animar triggers.
Resolve the Radagast trigger, creating a 3/3 Beast creature token.
Resolve the Animar trigger, putting a +1/+1 counter on it.
When Kiri-Onna enters the battlefield, its first ability triggers, returning itself from the battlefield to your hand.
Activate Phyrexian Altar by sacrificing the Beast token, adding {U}.
Repeat.

Combos with "Kiri-Onna"