If something is slinkiest, it is the most sly or sneaky.
Slinkiest can make people think of cats or spies, and it is usually not a good thing.
Examples:
The cat is the slinkiest animal in the house.
She gave me the slinkiest look, like she was up to something.
The slinkiest person in the room was watching everyone.
The slinkiest fox stole all the chickens!
The slinkiest spy snuck into the enemy's base without anyone noticing.
The slinkiest snake slithered through the grass without making a sound.