How can I get through very long and very dry, but also very useful technical documents when learning a new tool? Vulkan is a very useful API for rendering projects, and I would like to learn how to use it as it opens up new possibilities for doing some rendering tricks much more efficiently than in OpenGl.

I am having significant trouble learning it, however. It is a very complex API with many essential details. These details, while useful, are not interesting enough in and of themself to reliably hold my attention for long periods, even if I put in significant effort. I find when I go through the written tutorials that I get very distracted by almost anything. 

For example, when I was reading about its mechanism for selecting a GPU in a multi-GPU system instead of focusing on the syntax that I want to learn, I ended up thinking about all the implications of such a selection existing, compared to the fact that it does not in OpenGl. Distractions such as that end up drastically increasing the time that I need to spend on the reading, and skimming is not an option either as the details really are important. 

There are also diminishing returns as my ability to use will power to remain focused diminishes much more quickly than I would like it to (I can only get through maybe ~10 pages of this reading in a single sitting while maintaining the focus that I feel is necessary.)

This problem is not unique to Vulkan. I had the same problem, but to a much lesser extent, when learning OpenGl. In that instance, I was able to find video tutorials that explained the necessary concepts very succinctly. This helped both because the explanations were more succinct, with only the necessary information (including theory when appropriate) to use the API (and I could look at written alternatives when I wanted more details). 

When I attempted this for Vulkan, however, the only video tutorials that I could find were both outdated and contradicted the text tutorials in a few places, making me very weary of using them as I may pick up bad practices or outdated Vulkan. Video tutorials also work well for me as they keep on moving even if I get temporarily distracted, thus pulling my attention back. When reading, if I get distracted I automatically stop reading.

I would also like to note that this isn't an issue of lazyness; I am willing to put in significant time to do it, but I find that my ability to focus is quickly diminishing. 

As such, I ask: How can I learn Vulkan (Ideally, the advice will be applicable to other similar tasks as well) reasonably efficiently and how can I counter the described road-blocks?
Man, I'm right there with you. I understand completely your situation, as I've been there myself many times.

The key, I find, is not reading the tutorials. 

Instead, I pick a few projects - starting with something that's "hello, world" level. I google and read enough to be able to do that. Then I pick a slightly harder project - for Vulkan, maybe pick a scene of intermediate difficulty, and google and read enough to do that.

If you keep doing this, you very quickly obtain a practical base of knowledge. There are, however, disadvantages to this - obviously, there will be holes in your knowledge, and you could miss style guidelines depending on what you're looking at to write your code (e.g., when I first learned python, I came into it knowing how to program in javascript - so my first instinct was to write variable names in camelCase, and it was only after several years that I actually read PEP8 and changed to under_scores, though in my defense I didn't even realize style guides were a thing at the time). 

You might even wish to go through this approach, and then read through the tutorials with the perspective of someone who's "brushing up" - this might fill in the crevices the more trial and error method doesn't fill.

If, however, you wish to fully work through the documentation straight off, I'd recommend reading a paragraph/section, and writing down something about how you'd use what you just learned about in a real program - i.e., mentally applying the small details. You want to build up a 'web' of details, with lots of connections between the nodes, so that every node is much easier to 'get to' (remember). The more you know, the more you remember (as odd/obvious as that sounds).