My personal experience is that complicated proofs are usually discovered gradually: Someone first came up with a relatively simple proof of some result. Then, someone took that simple proof and added another idea to prove a stronger result. Next, someone added another idea or two to prove an even stronger (or different result), etc. Eventually, we end up with a very complicated proof of a very general and strong result.
Now, if someone tries to read the very complicated proof that was obtained at the end of that process, they will have a very difficult time: they are basically trying to digest the culmination of many years of research in one shot.
My personal strategy in such situations is to read the papers in chronological order. I try to read the paper that came first in this line of research - usually, that paper would be rather simple. Then, I try to understand the next paper, etc. Each time I read a paper in the line, I try to understand what was the new idea that the paper added. By the time I reach the last papers in the chain, what previously seemed to be a very complicated proof that I can barely understand turns out to be "what I already read + a simple idea or two".
This strategy can be very time consuming at first. However, within a single area of research, there are relatively few such "lines of research". Thus, after you implement this strategy a few times, you cover most of those lines. By that time, you will be able to read most of the papers in the area rather easily, since you will usually be familiar with the ideas they build on.
More generally, the reason that experienced researchers can read papers very quickly is that they usually already have good understanding of the area to which the paper belongs. When you have such understanding of the area, reading a new paper usually boils down to answering the question "what is the new simple idea that the paper adds to the area".
So, to sum up, if you want to be able to read papers quickly, first invest some time in gaining mastery of your research area. Once this is done, reading more papers should be rather easy.