This is an important question. Unfortunately, the question cannot even be properly framed within the Watchtower Society’s current understanding of the scripture in question. The reason being, according to the Watchtower’s interpretation the destruction of Jerusalem in the first century foreshadows the future fiery destruction of Babylon the Great – Christendom in particular. But if that were true, why would Jesus counsel his followers to take timely action to flee when Jerusalem was surrounded by enemies? Jehovah’s Witnesses are not part of Christendom, are they? And besides, Jehovah’s Witnesses have supposedly already heeded the command to “Get out of her my people.”
The only sensible interpretation, indeed, the only scripturally supported interpretation, is that Jesus intended “Jerusalem” to symbolize Jehovah’s earthly organization. This view has been discussed in a number of articles on e-watchman, the most recent being the essay entitled:
What is the Holy Place and the Great Tribulation?
So, from the standpoint of “Jerusalem” symbolizing Jehovah’s earthly organization how are we to understand Jesus’ instructions to flee to safety when the holy place faces desolation? The Hebrew Scriptures shed some light on that question. Take the 91st Psalm as an example. It opens by saying:
"Anyone dwelling in the secret place of the Most High will procure himself lodging under the very shadow of the Almighty One. I will say to Jehovah: 'You are my refuge and my stronghold, my God, in whom I will trust.'"
The Psalm goes on to enumerate various calamities that befall the world, including pestilence and adversities from war. These, of course, are the very things that Christ said would occur as an immediate prelude to the desolation of the holy place during the great tribulation.
The Watchtower has commented on the 91st Psalm a few times and applied it in some sort of bizarre symbolic way. One example that comes to mind, the thousands who “fall at your very side” due to the stalking pestilence are supposedly the masses who succumb to the spiritual plague of evolution.
The Society’s interpretation, though, is nonsensical in view of the fact that the various calamities that are described in the 91st Psalm are said to be
“retribution upon the wicked.” Is the theory of evolution God’s punishment upon the world? Of course not.
But the point is, the place to which Christians will flee when the modern holy place is destroyed will be
“the secret place of the Most High.” Such a place is a spiritual sanctuary and not a literal place. Likely, entry into Jehovah’s secret refuge at that time will involve recognizing and supporting the then-revealed sons of God. (See the essay
The Revelation of Christ and the Two Witnesses.