Joseph Smith's Kingly Birthright

One possible interpretation of D&C 86:8-10 is that Joseph Smith had the priesthood through birthright (see below for some complications*).

8 Therefore, thus saith the Lord unto you, with whom the priesthood hath continued through the lineage of your fathers--
9 For ye are lawful heirs, according to the flesh, and have been hid from the world with Christ in God--
10 Therefore your life and the priesthood have remained, and must needs remain through you and your lineage until the restoration of all things spoken by the mouths of all the holy prophets since the world began. 

An early hint of JS' beliefs about his lineage come from 2 Ne 3, which teaches that JS is a descendant of Joseph (11th son of Israel), and though the lineage of Ephraim is one of leadership, it's not apparent that there is a lineal priesthood associated with it like there is for the Levites or the sons of Aaron.

However, a Smith family lineal priesthood authority is actually well attested. JS established the position of Patriarch of the church, which originally was something akin to second in command, as a lineal position given to the eldest in a direct line from Joseph Smith Sr. This clear example of a lineal priesthood eventually disappeared when the position of church Patriarch was not filled after Eldred Smith.

The position of Patriarch to the church is only half of the story. D&C 113 states, "What is the rod spoken of in the first verse of the 11th chapter of Isaiah, that should come of the Stem of Jesse? Behold, thus saith the Lord: It is a servant in the hands of Christ, who is partly a descendant of Jesse as well as of Ephraim, or of the house of Joseph, on whom there is laid much power." It is common in Mormon thought to believe these verses apply to Joseph Smith, and that seems to be a correct assumption. The line of Jesse refers to the kingly line of David, and significantly, JS prophesied "the throne and kingdom of David is to be taken from him and given to another by the name of David in the last days, raised up out of his lineage," which apparently referred to one of JS' offspring. He made this clear when he prophesied that his unborn son, David, would be a "church president and king over Israel" (see D. Michael Quinn, The Mormon Hierarchy: Origins of Power, p. 644 April–May 1844).

In Mormon theology, a King in the kingdom of Israel is a priesthood position. Notably, JS himself was ordained as a King in this sense in the Council of Fifty, also known in revelation as the "The Kingdom of God and His Laws with the Keys and Power thereof, and Judgment in the Hands of His Servants, Ahman Christ." According to Nauvoo theology the priesthood role of King was the ultimate leader of the Church, and according to contemporary accounts, Hyrum Smith was to fill JS' shoes should he die. All of this together gives a pretty clear answer to the lineal priesthood possibly hinted in D&C 86. The Smith family was a royal family in Israel destined to lead the restoration.

*Notes on D&C 86:

Section 86 generally and these specific verses address a plural audience, an important fact that I missed when I first wrote this.

 

Looking into the plural aspect of the revelation has already turned up some interesting information, but before I launch into that, I'd just like to point out that the most significant idea of this post, that Joseph Smith believed himself to be of the lineage of Jesse/David and that his unborn son would be the new King David leading the church (and probably the world or something like that), is true whether D&C 86 is referring specifically to Joseph or not. In terms of the plural address in D&C 86, some pertinent information about audience is found in the source document in Revelation Book 2 on the JSP website. A note, original to the document, at the end of the revelation reads:

Kirtland December 6th. A[D] 1932 given by Joseph the seer and writen by Sidney the scribe an[d] Councellor, & Transcribed by Frederick assistent scribe and counceller

Frederick William's transcription occurred sometime in January or February of 1833 according to the JSP source note, which means the only two names specifically tied to this revelation's reception are Joseph and Sidney. Essentially, there is an argument to be made that the plural address of this revelation is specifically to Joseph Smith Jr. and Sidney Rigdon. If true, this could be seen as a follow up to an event earlier in 1832 in which Sidney Rigdon preached that the keys of the kingdom had been taken from the church, after which JS corrected him. This was no small matter apparently, and JS prophecied that Rigdon would be afflicted by Satan. Some weeks later Rigdon was spiritually attacked while laying in bed, and then still later Rigdon was reordained by JS, who was satisfied with Rigdon's repentance. From start to finish, this all apparently happened in July of 1832. Whatever Rigdon's doubts about the keys may have been, would have been nullified by a right to priesthood if they "were lawful heirs according to the flesh."

Though, I don't know of any specific priesthood authority assigned to Rigdon's lineage, I still think this 1832 revelation could be an early indication that there was a lineal priesthood in the Smith family, which would be made explicit and irrefutable later on with the establishment of the lineal position of Patriarch to the Church. 

Looking at JSP website also I came across this interesting 1835 tie-in from D&C 107:

39 It is the duty of the Twelve, in all large branches of the church, to ordain evangelical ministers, as they shall be designated unto them by revelation—
40 The order of this priesthood was confirmed to be handed down from father to son, and rightly belongs to the literal descendants of the chosen seed, to whom the promises were made.

 This ties patriarchal order of priesthood to "literal descendants of the chosen seed," obviously the Smith family if we judge by the office of presiding patriarch.

Anyways, the plural address of D&C 86 definitely muddies the waters. Either way, the lineal priesthood position of presiding patriarch emerges in the Smith family, and the most interesting piece stands independently of D&C 86, which is that Joseph appeared to have believed that his priesthood office of King was tied to a lineage traced back to King David, and that JS' son David would someday fill that role.