Espeon is actually really more of a feline. All others are more canine-ish because of the shape of all their tails. I mean dogs, cats, foxes(although not really, in my opinion) are all canines and the Eeveelutions revolve around these species anyway right?
Here is what I'm going with:
Eevee- Fennec Fox
Flareon- half cat, half Fox-ish
Vaporeon- Cat with Fish traits
Umbreon- Iffy about this one, I want to say dog, but I got a rabbit feeling for him.
Leafeon- Cat (Listen to her cry in-game, that's enough to prove it)
Glaceon- I'm going with cat on this one as well
Realistic, Eevee is composed of multiple Mammal genetic species, so it's tough really judging which Pokemon is for sure which animals.