The entire poem uses alliteration, onomatopoeia and rhyme to great effect to convey the fiesty nature of an active cat.
Phrases like "sleeky flatterer" recognize the long, slim body shape of a healthy cat rubbing against ones legs to indicate affection and appreciation of the person's presence. "Green-eyed scratcher" could simply be indicating the actual color of the eyes of the cat being described, or could be a symbolic reference to a cat's jealousy as demonstrated by scratching an object in order to get revenge for being ignored or to get attention returned to itself.
"Whiskery spitter" acknowledges the long facial whiskers possessed by most cats, framing the hisses and spits and howls that cats produce when they are displeased or worse.
sorry i rated this answer "poor" by mistake. It is exellent. thank you.