Of course Jesus' gospel is based on salvation which is why Paul preached the gospel of the kingdom.
Jesus said those who are born of the flesh are sarx (flesh) and those who are born of the Spirit are pneuma (spirit)
Paul NEVER preached the gospel of the kingdom! He could not have even been forgiven under it!
Matthew 12:31 Wherefore I say unto you, All manner of sin and blasphemy shall be forgiven unto men: but the blasphemy against the Holy Ghost shall not be forgiven unto men.
Matthew 12:32 And whosoever speaketh a word against the Son of man, it shall be forgiven him: but whosoever speaketh against the Holy Ghost, it shall not be forgiven him, neither in this world, neither in the world to come.
It's one of the reasons we know that the Lord was going to do something different and showed it by the saving of Paul (then Saul).
1 Timothy 1:12 And I thank Christ Jesus our Lord, who hath enabled me, for that he counted me faithful, putting me into the ministry;
1 Timothy 1:13 Who was before a blasphemer, and a persecutor, and injurious: but I obtained mercy, because I did it ignorantly in unbelief.
1 Timothy 1:14 And the grace of our Lord was exceeding abundant with faith and love which is in Christ Jesus.
1 Timothy 1:15 This is a faithful saying, and worthy of all acceptation, that Christ Jesus came into the world to save sinners; of whom I am chief.
1 Timothy 1:16 Howbeit for this cause I obtained mercy, that in me first Jesus Christ might shew forth all longsuffering, for a pattern to them which should hereafter believe on him to life everlasting.