As an English person I would say 'He is in advance age' is not correct. As you say it does need to be either "he is of an advanced age' or '...at an advanced age' but he could be '...in old age'
In another example, "Mio nonno è di età avanzata," the English translation required the article "an" before "advanced age." Why is the article not required in this one?
I had: "she is of an advanced age" and it was oké
old age = età avanzata