When Geralf's Messenger dies, its undying ability triggers, returning it from your graveyard to the battlefield with a +1/+1 and a vigilance counter on it.
When Geralf's Messenger enters the battlefield, it triggers, causing target opponent to lose 2 life.
When Kitchen Finks dies, its persist ability triggers, returning it from your graveyard to the battlefield with a -1/-1 and a vigilance counter on it.
When Kitchen Finks enters the battlefield, it triggers, causing you to gain 2 life.
Activate Tayam by paying ({3} magic symbol) and removing the +1/+1 counter from Geralf's Messenger, the -1-1 counter from Kitchen Finks, and a vigilance counter from any creature you control, milling yourself three cards then returning any permanent card with mana value 3 or less from your graveyard to the battlefield.
Repeat.
Results
Infinite blinking of creatures with mana value 3 or less on the battlefield or in the graveyard or library.
Infinite colorless mana.
Infinite death triggers.
Infinite ETB.
Infinite lifegain.
Infinite lifegain triggers.
Infinite lifeloss.
Infinite LTB.
Infinite sacrifice triggers.
Infinite self-mill.
Put all permanent cards with mana value 3 or less from your graveyard or library onto the battlefield.