No.
It's not possible for Zebras to throw up because they do not have the mechanism inside them like humans and some other animals do.
If a Zebra eats anything that is poisonous to them then it can easily be fatal to them as they won't be able to vomit up the thing that they ate that was poisonous.
Zebras belong to the same family as equine and horses which cannot throw up either.
Neither the Zebras or the horses have the nerve muscles or muscles to allow them to throw up so without those nerve muscles and muscles the ability to throw up is not possible.