Thank you for the Biblical question, “When will Matthew 24:14 be completed? And this gospel of the kingdom will be preached in the whole world as a testimony to all nations, and then the end will come.”
Matthew 24 is a difficult passage to interpret with theologians having varying viewpoints from post-millennialists, amillennialists, and even pre-millennialist. Within that discussion would include the interpretation of the Gospel of the Kingdom as being the same as the Gospel of Salvation. Although they are related, there are differences and those differences may have been considered by another question on Quora or on the Christian Corner.
There are three time references to the preaching to the whole world:
A. One view is that the proclamation to the whole world was completed by the end of the first century (Matt. 24:34).
B. One view is that the proclamation to the whole world is being completed until the rapture of the Christians (Acts 1:8).
C. One view is that the proclamation to the whole world will be completed during the Great Tribulation Period just before the Second Coming of Christ (Matt. 24:14–15).
Each of the viewpoints have its pros and cons. My understanding of the fulfillment of the preaching of the Gospel of Kingdom is during the Great Tribulation Period. The 144,000 witnesses will be declaring the return of the Messiah for Israel and to the nations. The two witnesses will be viewed by the whole world when their message is proclaimed and televised to every nation and people group. It is in the Great Tribulation that the persecution and suffering may exceed the Holocaust suffering of the Jews. This persecution extends to both Jews and to the agnostics/atheists who will be forced to worship the Antichrist (Rev. 13:11–18).
It can be said that in the last 75 years that it is literally possible to broadcast live news to every nation and people group with our modern technology. This is even more true today that goes beyond television or radio to iphone whereby most of the world has access to them except for the most primitive people group in the jungles.
The rapture of Christians, if one holds to that position, lays the foundation for the rise of the Antichrist and the Jews seeing the fulfillment of the Old Testament prophecies. Presently for the most part the Jews are not actively proclaiming the return of the Messiah although they are preparing to rebuild the Temple with its furnitures. My understanding that the end will come as the Great Tribulation begins with the rapture of the Christians.
SUMMARY: The end will come when the Gospel, however, one may define it, when it reaches every nation and people group. In many ways, we are on the verge of that reality today. The Lord’s coming is nearer than when we first heard it.
For more perspectives: