What is the kingdom phylum class order family genus and species of a monkey?

Completely depends exactly which monkey you mean, but the generalised answer (they're the same for all monkeys) is:

Kingdom: Animalia

Phylum: Chordata

Subphylum: Vertebrata

Class: Mammalia

Order: Primates

Suborder: Haplorrhini

If you know the specific type of monkey, you should be able to find the family, genus and species.
Animal - Monkey

Domain - Eukarya

Kingdom - Animalia

Phylum - Chordata

Class - Mammalia

Order - Primates

I'm not sure about the family, genus, or species. I think that depends on the type of monkey.

Hope this helps! :)