you need to consider whether your flash can reach the distance ... normally we shoot animals using 200mm upwards ... with this distance, your flash will not be able to reach...
if you are talking about during performances, if flash is prohibited, they will announce it. Usually these are the more dangerous performances. similarly you need to consider our distance from the animals.
When you say "appropriate", are you asking if they allow flash photography, or are you asking should we use flash because it may hurt the cute animal's eyes and they see a blur and may fall off the tree?
that's sorta night safari whereby flashes ain't allowed in the first place. i understand your stand on flashes on animal and personally, i wouldn't use flash at all.
flashes in the zoo would most probably be used for filling. personally, animals that are within 1m of range, i would never use flash on them. they might be sensitive to light or something and we might hurt them without realising it.
i shot pictures in the zoo mainly using 1.8 or something. for lions and such, tripods and long telezoom lens? well, we can't stop anyone here but just to advise