The Pedegree of Jeremiah.

David had two high priests: Zadok of the line of Aaron and Abiathar of the line of Eli (the line of Moses according to F.M. Cross)

At David's death Solomon banished Abiathar to Anathoth

1 Kings 2:26
The king said to the priest Abiathar, "Go to Anathoth, to your estate; for you deserve death. But I will not at this time put you to death, because you carried the ark of the Lord GOD before my father David, and because you shared in all the hardships my father endured."

The line of Zadok continued in the position of the high priest down to Hezekiah. The line of Abithar continued as defrocked priests, living in and around Anathoth.

Hezekiah's son, Manasseh, slaughtered many of the priestly establishment.

2 Kings 21:16
Moreover Manasseh shed very much innocent blood, until he had filled Jerusalem from one end to another, besides the sin that he caused Judah to sin so that they did what was evil in the sight of the LORD.

Manasseh reigned for 55 years. That means that only the very, very old could remember the true worship of God under Hezekiah by the time of his death. Except , of course, for the clandestine religious, some living in Anathoth.

Manasseh's son Amon was 22 when he assumed the throne. But his reign was short lived.

2 Kings 21:23-24
The servants of Amon conspired against him, and killed the king in his house. But the people of the land killed all those who had conspired against King Amon, and the people of the land made his son Josiah king in place of him.

Under Josiah the worship of God resumed under the leadership of a new family of priests. One of those priests discovered a book in the temple. Some scholars believe this book to be the core of our present book of Deuteronomy.

2 Kings 22:8
The high priest Hilkiah said to Shaphan the secretary, "I have found the book of the law in the house of the LORD." When Hilkiah gave the book to Shaphan, he read it.

The priest who found the book of the law was Hilkiah, presumably the high priest who alone could converse directly with the shaphan.

Now we turn to Jeremiah.

Jeremiah 1:1-2
The words of Jeremiah son of Hilkiah, of the priests who were in Anathoth in the land of Benjamin, to whom the word of the LORD came in the days of King Josiah son of Amon of Judah, in the thirteenth year of his reign.

Hypothesis:
1. That the people who placed Josiah on the throne were the "resistance" movement under Manassah.
2. That when the murderers of Amon were rounded up and they gained power in the land, they reinstated the priestly line of Moses/Eli/Abithar and their hight priest was Hilkiah.
3. That this same Hilkiah is the "Hilkiah of the priests who were in Anathoth" that is said to be the father of Jeremiah.