If one describes a person as "the son of my father’s brother," how is that person related to the speaker?

The description "the son of my father’s brother" refers to a familial relationship known as a cousin. In this case, the speaker's father's brother is the speaker's uncle, and the son of that uncle would indeed be the speaker's first cousin. Cousins are typically the children of a person's aunts and uncles, making this relationship direct and clear.

In contrast, an uncle is a brother to one’s parent, a brother is a male sibling, and a nephew is the son of one’s brother or sister. Thus, the relationship identified in the question aligns perfectly with the definition of a cousin.