According to Two Kingdom theology, could a man hold both secular and spiritual office?

The Book of Concord is the seminal reference for Lutheran theology, and is a collection of statements from the period. Some Lutherans ascribe to all of the BOC, others argue about applicability of various documents beyond the Augsburg Confession. Here one relevant text from the Augsburg Confession,

Article XVI: Of Civil Affairs.

1] Of Civil Affairs they teach that lawful civil ordinances are good works of God, and that 2] it is right for Christians to bear civil office, to sit as judges, to judge matters by the Imperial and other existing laws, to award just punishments, to engage in just wars, to serve as soldiers, to make legal contracts, to hold property, to make oath when required by the magistrates, to marry a wife, to be given in marriage.

3] They condemn the Anabaptists who forbid these civil offices to Christians.

4] They condemn also those who do not place evangelical perfection in the fear of God and in faith, but in forsaking civil offices, for 5] the Gospel teaches an eternal righteousness of the heart. Meanwhile, it does not destroy the State or the family, but very much requires that they be preserved as ordinances of God, and that charity be practiced in such 6] ordinances. Therefore, Christians are necessarily bound to obey their own magistrates 7] and laws save only when commanded to sin; for then they ought to obey God rather than men. Acts 5:29.

Here we have an explicit statement that individual Christians may hold state office, in the Augsburg Confession. The BOC continues with Defenses and Solid Declarations, which essentially repeat the explanation in the AC.

The Sixteenth Article [of the Augsburg Confession] the adversaries receive without any exception, in which we have confessed that it is lawful for the Christian to bear civil office, sit in judgment, determine matters by the imperial laws, and other laws in present force, appoint just punishments, engage in just wars, act as a soldier, make legal contracts, hold property, take an oath, when magistrates require it, contract marriage; finally, that legitimate civil ordinances are good creatures of God and divine ordinances, which a Christian can use with safety. 54] This entire topic concerning the distinction between the kingdom of Christ and a political kingdom has been explained to advantage [to the remarkably great consolation of many consciences] in the literature of our writers, [namely] that the kingdom of Christ is spiritual [inasmuch as Christ governs by the Word and by preaching], to wit, beginning in the heart the knowledge of God, the fear of God and faith, eternal righteousness, and eternal life; meanwhile it permits us outwardly to use legitimate political ordinances of every nation in which we live, just as it permits us to use medicine or 55] the art of building, or food, drink, air.

This statement here makes reference to Luther's earlier writing on Two Kingdoms with "in the literature of our writers."

Twice the BOC explicitly states that "a Christian" may serve in civil office. Any speculation that there could be some distinction in Lutheranism between what a pastor may do and what "a Christian" may do can easily be disproven by reading the appropriate sections.

To explain it further, consider someone with dual vocations of pastor and sheriff. I've seen Two Kingdoms described as "hat you're wearing." Such a dual-vocation person would proclaim forgiveness of sins in church, and arrest bad guys in the saloon. It is about separation of jobs. Our hypothetical person shouldn't arrest people for failing to attend church, nor should he apply forgiveness of sins during the arrest of a bad guy.

In the course of listening to White Horse Inn broadcasts I've consistently heard the participants refer back to John Calvin when commenting on Two Kingdom Theology. I think it very useful to look at how Mike Horton treats Cavlin's comments on the Two Kingdoms in his recent book on Calvin. If we assume that Horton is in agreement with Calvin, then I think Horton's interpretation of Calvin's views is a valid representation of what a modern Two Kingdoms view looks like.

"For Calvin, they [secular government and the church] are side by side: distinct by not separate.", — Calvin on the Christian Life, pg 221, Mike Horton, Crossway, 2014

So, yes. A Christian is a member of both kingdoms and is expected to participate in both. If he is apt to govern, then he should govern. If he is apt to be an elder, than he should be an elder.

Calvin believed that secular government also was bound to protect the true church, so mapping Calvin into modern politics is awkward. Formal religion is being pushed out of Government.

Calvin covers his views in The Institutes of the Christian Religion right after man's freedom and before civil government. You could go to the source, if you so chose.

This is an interesting question. Bear with me as I attempt to build a bit of Confessional background to my answer.

It's clear from Article 5 of the Augsburg Confession that the office of the ministry was instituted by God to preach the Gospel and administer the Sacraments (http://bookofconcord.org/augsburgconfession.php#article5). This is God's "Right Hand Kingdom or Realm." See also articles 7 and 8 in the Confession. Then, the Confession notes that no one should do these things "publicly" (i.e. in the name of a congregation) unless he be regularly (or rightly) called (Article 14).

Then, Article 16 talks about Civil Affairs (http://bookofconcord.org/augsburgconfession.php#article16). This is God's "Left Hand Kingdom or Realm" of civil government. It's interesting that in this Article there is no distinction between the various offices; i.e. "it is right for Christians to bear civil office, to sit as judges, to judge matters by the Imperial and other existing laws, to award just punishments, to engage in just wars, to serve as soldiers, to make legal contracts, to hold property, to make oath when required by the magistrates, to marry a wife, to be given in marriage." In this Article, bearing a civil office is lumped in with marrying a wife. Then, you have Article 23 later which states it is right and proper for "priests" (i.e. those holding the office of the ministry) to marry. So, there's a logical connection then that seems to state that those who hold the office of the ministry could, theoretically, hold a civil office.

However, Article 28 (http://bookofconcord.org/augsburgconfession.php#article28) goes into more details about the distinctions between God's Left Hand Kingdom (civil government) and His Right Hand Kingdom (the Church). Both are instituted by God to care for His world; the Left Hand to enforce order, keep peace, pursue justice; the Right Hand to proclaim the Gospel by which people are saved by grace through faith.

A key quote from this Article is: "If bishops have any power of the sword, that power they have, not as bishops, by the commission of the Gospel, but by human law having received it of kings and emperors for the civil administration of what is theirs. This, however, is another office than the ministry of the Gospel."

The point is that bishops may have their office in the Right Hand realm as well as their office in the Left Hand realm, but that they have to understand that these are separate offices with different roles. So, the Confessions seem to recognize that the possibility exists for one person to hold both a Left Hand ("secular" or "civil) office and a Right Hand ("spiritual" or the office of the ministry).

That said, is this advisable, even if it is technically allowed? That's probably a separate question that what was originally asked. On the one hand, it would be hard for a pastor to separate his office in the ministry with his office as, for example, a mayor. On the other hand, if a pastor may get married, perform marriages, even serve as a soldier (e.g. a military chaplain), then why can he not serve as a mayor?