Cast Burning Inquiry by paying {R}.
Birgi triggers, adding {R}.
Resolve Burning Inquiry, causing each player to draw three cards and discard three cards at random.
Cast Burning Inquiry from your graveyard for its escape cost by paying {R} and exiling 3 cards from your graveyard.
Repeat from step 2.

Infinite draw triggers for all players

Infinite self-mill

Near-infinite mill

Near-infinite self-discard triggers

Near-infinite storm count

Birgi, God of Storytelling // Harnfel, Horn of Bounty

Underworld Breach

Burning Inquiry

Cast Burning Inquiry from your graveyard for its escape cost by paying {R} and exiling three other cards from your graveyard.
Storm-Kiln Artist triggers, creating a Treasure token.
Resolve Burning Inquiry, causing each player to draw three cards and discard three cards at random.
Activate the Treasure token by tapping and sacrificing it, adding {R}.
Repeat.

Infinite self-discard triggers for all players

Near-infinite magecraft triggers

Storm-Kiln Artist

Cast Burning Inquiry for its escape cost by paying {R} and exiling three cards from your graveyard.
Runaway Steam-Kin triggers, putting a +1/+1 counter on itself.
Resolve Burning Inquiry, causing each player to draw three cards and discard three cards at random.
Repeat steps 1-3 two additional times.
Activate Runaway Steam-Kin by removing three +1/+1 counters from it, adding {R}{R}{R}.
Repeat until you have less than three cards in your library.
If Thassa's Oracle is in your hand, cast it by paying {U}{U}.
If Thassa's Oracle is in your graveyard, cast it for its escape cost by paying {U}{U} and exiling three cards from your graveyard.
Thassa's Oracle enters the battlefield, causing you to win the game.

Infinite draw triggers

Infinite looting

Win the game

Runaway Steam-Kin

Thassa's Oracle

Cast Underworld Breach by paying {1}{R}.
Kykar, Wind's Fury triggers, creating a 1/1 Spirit creature token with flying.
Underworld Breach resolves.
Activate Kykar by sacrifice a Spirit token, adding {R}.
Cast Burning Inquiry by paying {R}.
Kykar, Wind's Fury triggers, creating a 1/1 Spirit creature token with flying.
Resolve Bruning Inquiry, causing each player to draw three cards, then discard three cards at random.
Activate Kykar by sacrifice a Spirit token, adding {R}.
Cast Burning Inquiry from the graveyard for its escape cost by paying {R} and exiling three other cards from your graveyard.
Repeat until you have two or fewer cards in your library.
Cast Thassa's Oracle from your graveyard for its escape cost by paying {U}{U} and exiling three other cards from your graveyard.
Thassa's Oracle enters the battlefield and triggers, causing you to win the game.

Exile your library

Kykar, Wind's Fury

Cast Burning Inquiry for its escape cost by paying {R} and exiling three cards from your graveyard.
Runaway Steam-Kin triggers, putting a +1/+1 counter on itself.
Resolve Burning Inquiry, causing each player to draw three cards and discard three cards at random.
Repeat steps 1-3 two additional times.
Activate Runaway Steam-Kin by removing three +1/+1 counters from it, adding {R}{R}{R}.
Repeat until you draw from an empty library, causing you to win the game.

Laboratory Maniac

Jace, Wielder of Mysteries

Combos with "Burning Inquiry"