What special knowledge was John taught as a priest's son?
John was not only taught special knowledge, but he was also allowed special privileges as well. For example, John was allowed to go to the Dead Places and gather metal.
I myself was allowed to go into the dead houses and search for metal.
John was also allowed to study the Dead Places on his own and investigate them further. He tells the reader that he attempted to learn the way of those houses.
The knowledge seems to be basic medicine and first aid treatment. John describes it as chants and spells, but then describes that he is able to stop the bleeding from larger wounds.
I was taught the chants and the spells—l was taught how to stop the running of blood from a wound and many secrets.
Probably the most significant thing that John learned to do as the son of a priest (and future priest) was to read and write.
I was taught how to read in the old books and how to make the old writings—
The reason it is significant is because he is able to understand what New York City really was when he goes on his journey east. He understands that it was a great city of men, not gods. He understands that the people that lived there had great knowledge, and John plans to bring it back to his people and begin rebuilding all of the lost knowledge.