I will offer two compatible interpretations based on the theology of Emanuel Swedenborg (1688-1772) and the churches that accept his theology.
1. "Quickly" means "definitely"
Here is how Swedenborg interprets the same phrase in Revelation 1:1:
Things which must shortly take place. This symbolically means that they must surely come to pass to keep the church from perishing.
"Which must shortly take place" does not mean that the things
predicted in the book of Revelation are going to happen immediately or
quickly, but that they will happen surely, and that unless they come
to pass, the church will perish.
In the Divine view, and so in the spiritual sense, time does not
exist, but instead of time, state. And because "shortly" has to do
with time, it symbolically means certainty and that something will
happen before its time. For the book of Revelation was written in the
first century, and seventeen centuries have now gone by, from which it
is apparent that "shortly" means, symbolically, what corresponds to
it, which is certainty. (Apocalypse Revealed #4)
You can read the full section from Apocalypse Revealed, including some supporting passages from the Bible, here.
Here is the basic idea:
God exists outside of time. And there is no time as we know it on the spiritual level of reality. So if we read the Bible from a spiritual perspective, every mention of time in the Bible means something other than time, because spiritually there is no time.
When it comes to "quickly" or "soon," the idea conveyed spiritually is that this is definite and inevitable. It's going to happen. No doubt about it!
2 Peter 3 conveys this meaning powerfully. Peter's appeal is not a temporal one. He is not saying that it's going to happen at a specific time. Rather, he's saying that it's going to happen, so we must be prepared for it. Don't delay repenting, or it may be too late!
So the spiritual force of the Lord saying "I am coming quickly" is that this is definitely going to happen, so you had better not dawdle, but prepare yourself for it through repentance and accepting the Lord into your life.
2. For individuals, Jesus does come quickly
The book of Revelation as a whole, and other places in the New Testament that speak of Jesus' coming, are usually interpreted as applying to Jesus coming on the scale of the whole world and its people. And that is a perfectly valid interpretation.
However, for each one of us individually, Jesus, the Apocalypse, and the judgment also comes. And for us individually, that effectively happens on the day that we die.
Whether you believe in a universal judgment at some future date or individual judgment immediately after death, it really doesn't matter for us as individuals.
For us as individuals, the day we die is the day that our judgment is made certain. At that point, we have lived our lives. We have either repented or not repented. We have either believed in the Lord or not believed in the Lord. We have either obeyed God's commandments or not obeyed God's commandments.
No matter what our particular church or religion says we must do to be saved, there is a deadline to it (assuming there is no reincarnation, as nearly all Christians believe).
That deadline is our death.
So when Jesus says, "I am coming quickly," or "I am coming soon," for us individually it means, we do not know the day of our death. It could happen next year, next week, tomorrow, or tonight. We may think we have plenty of time. But death could come to us suddenly.
This is what Jesus was talking about in the Parable of the Rich Fool in Luke 12:13-21, which concludes with:
But God said to him, "You fool! This very night your life will be
demanded from you. Then who will get what you have prepared for
This is how it will be with whoever stores up things for themselves
but is not rich toward God. (Luke 12:20-21)
So for us individually, the force of "I will come soon" or "quickly" is that it's definitely going to happen, we don't know when, but it could be any ordinary day that we get up thinking we're about to have another boring day.
The message of "I am coming quickly," then, is not to dawdle or delay, but to do today what we need to do to prepare ourselves for eternity, and to keep doing that each day as if it is our last--which it might just be.
Once again, this interpretation is based on the theology of Emanuel Swedenborg and the churches that follow his teachings.