With all three cards in play, pay 3 mana to activate Soulbright Flamekin's ability and add 8 red mana.
Activate Mirage Mirror to copy itself.
Retain priority and activate Mirage Mirror again, copying Soulbright Flamekin again.
Let the first copy resolve and Mirage Mirror will become a copy of Soulbright Flamekin
With the second copy on the stack, activate the Soulbright Flamekin copy's ability 3 times to add 8 red mana.
Let the second copy resolve, Mirage Mirror will become an artifact again.
Repeat the process for infinite mana