I'm assuming that by "learning to write in English" you mean actually writing meaningful texts in English, rather than just copying out words without any idea of their meaning.
However, if the end goal is just proving that the Zoblings are intelligent, then they have better options: mimicking humans sounds/actions to show they understand human are doing something, coordinating themselves to perform some patterns like tapping their feet a certain number of times over and over again until the humans pay attention, etc. Unless the Zoblings can get a human to give examples to words in the dictionary or find some translation of a few words into the Zobling's language, they won't be able to decipher the meaning of what the weird symbols in the dictionary are. It's not even enough to hear the humans speak, since the Zoblings will have no way to understand how any letter is pronounced and thus can't match spoken words to the written words. We were only able to understand these hieroglyphs when we found the Rosetta Stone, since we then had a reference for what the symbols mean, not just what set of symbols they had. The Zoblings are going to have the same problem we had when trying to understand the Egyptian hieroglyphics.
The above could be a dictionary or a grocery list, there is no difference to you. Given that you can recognize that these symbols have meaning to the Egyptians, can you learn to at least write in it without the aid on an Egyptian?