Activate Blasting Station by tapping it and sacrificing Kitchen Finks.
When Kitchen Finks dies, its persist ability triggers, returning Kitchen Finks from your graveyard to the battlefield with a -1/-1 counter on it.
When Kitchen Finks enters the battlefield, it and Blasting Station trigger.
Resolve the Blasting Station trigger, untapping it.
Resolve the Kitchen Finks trigger, causing you to gain 3 life.
Cleric Class triggers, putting a +1/+1 counter on Kitchen Finks.
Resolve the Blasting Station ability from step 1.
Repeat.
This loop transforms the humble life-gain of Kitchen Finks into a lethal battery by turning its inevitable return from the graveyard into a self-sustaining engine. Every time the Finks die and persist brings them back with a -1/-1 counter, Blasting Station untaps from the creature entering the battlefield so you can sacrifice them all over again. Cleric Class acts as the crucial catalyst here: its replacement effect pumps up the life you gain from the Finks, and its triggered ability drops a +1/+1 counter onto the returning creature to immediately cancel out its -1/-1 counter. This neutralizes persist's limitation, allowing the Finks to bounce back indefinitely while Blasting Station peppers your opponents with endless damage.