Declare the creature with Breath of Fury attached as an attacker.
Dogmeat's second ability triggers, creating a 2/2 Cat creature token with haste due to Jinnie Fay.
Deal combat damage using the creature that has Breath of Fury attached.
Breath of Fury triggers, causing you to sacrifice the creature it is attached to, then attach Breath of Fury to the Cat token, then causing you to untap all creatures you control and to get an additional combat phase after this one.
Repeat each combat phase.

Infinite combat damage

Infinite combat phases

Infinite death triggers

Infinite ETB

Infinite LTB

Infinite mana creatures you control can produce

Infinite sacrifice triggers

Infinite untap of creatures you control

Jinnie Fay, Jetmir's Second

Dogmeat, Ever Loyal

Breath of Fury

Activate Phyrexian Altar by sacrificing Dogmeat, adding {W}.
When Dogmeat dies, Gift of Immortality triggers, returning Dogmeat to the battlefield from your graveyard.
When Dogmeat enters the battlefield, its first ability triggers, causing you to mill five cards and return Gift of Immortality to your hand from your graveyard.
Cast Gift of Immortality by paying {W} due to Mana Matrix, attaching it to Dogmeat.
Repeat.

Infinite self-mill

Infinite storm count

Gift of Immortality

Phyrexian Altar

Mana Matrix

Activate Phyrexian Altar by sacrificing Dogmeat, adding {W}.
When Dogmeat dies, Gift of Immortality triggers, returning Dogmeat to the battlefield from your graveyard.
When Dogmeat enters the battlefield, its first ability triggers, causing you to mill five cards and return Gift of Immortality to your hand from your graveyard.
Cast Gift of Immortality by paying {W} due to Semblance Anvil, attaching it to Dogmeat.
Repeat.

Semblance Anvil

Activate Phyrexian Altar by sacrificing Dogmeat, adding {W}.
When Dogmeat dies, Gift of Immortality triggers, returning Dogmeat to the battlefield from your graveyard.
When Dogmeat enters the battlefield, its first ability triggers, causing you to mill five cards and return Gift of Immortality to your hand from your graveyard.
Cast Gift of Immortality by paying {W} due to Council of the Absolute, attaching it to Dogmeat.
Repeat.

Council of the Absolute

Combos with "Dogmeat, Ever Loyal"