What is the promise God made to David in 2 Samuel 7 about the kingly line?

God promised David that He would raise up David's own seed after him and establish His kingdom. That promised Son would build a house for God's name, and God would establish the throne of His kingdom forever, carrying the kingly line from David down to Christ the King.

Les explains from 2 Samuel 7:12-13 that God told David He would not intervene in the physical element of death; David would sleep with his fathers, but God would set up David's seed after him, proceeding out of his bowels, that is, his own Son. God says, 'I will establish His kingdom. He shall build a house for My name, and I will establish the throne of His kingdom forever.' Les ties this to the promise of the kingly line that would run all the way from David down to the coming of Christ the King. He calls it the house of David. In verse 14 God adds, 'I will be His Father, and He shall be My Son'; if He commits iniquity, God will chasten Him with the rod of men and with the stripes of the children of men. Les notes Israel repeatedly experienced that discipline, as in the book of Judges, yet God never gave up on them.

2 Samuel 7:13

He shall build an house for my name, and I will stablish the throne of his kingdom for ever.

2 Samuel 7:14

I will be his father, and he shall be my son. If he commit iniquity, I will chasten him with the rod of men, and with the stripes of the children of men:

What is the promise of the kingly line in 2 Samuel 7:12-13?

God promised to set up David's seed after him, a descendant proceeding from his bowels, that is, His own Son. He would establish that Son's kingdom. This Son would build a house for God's name, and God would establish the throne of His kingdom forever, extending the kingly line from David to Christ the King.