It took a long time, but now I can easily read for an hour. My normal routine now is to wake up an hour before I have to and read for an hour or so, and then again in the evening read for an hour or so. Reading a book in the morning is really a great way to start the day, I find. I still prefer ending the day falling asleep to the office or something like that.
One of the things that has really worked for me, other than training the practical side of reading for prolonged amounts of time with focus, is to get used to preferring long pieces instead of the quick fixes that is mostly what's online. Before I wanted the quick reads, they felt like I achieved things. Now I want the long pieces, the books, the journalistic marvels that took years to produce and an hour or more to really go through properly. It took time to get here, getting rid of the fear of missing out - which I'm still working on - and understanding that all sorts of things happen in the "now", but almost anything of importance and substance is best "consumed" at a distance - maybe a week or more after it happens. That's especially true for news, except for the odd once that you want to know about right now, but I feel like when that happens, word will get to your from other paths, like family, friends and so on contacting you if it's that important. Any news that is not important enough to warrant your attention after it's a week old, is it really worth knowing anyway?
For that matter, programming's like that too. After a 15-20 minute chunk I'll usually feel a strong urge to go check HN (clearly, I'm in one of those now). If I can resist that urge enough, and have long enough blocks of time (challenging with a kid now), I can find myself coding for several hours straight until I finish the change I was working on.
I hope it isn't pointless self help book. I used to be exactly like that until I realized how pointless they are.
Even just another room or nook works, or the public library, so long as all you do there is read. You'll begin to associate that spot with reading and have an easier time getting into the reading mindset.
Have you tried graphic novels? I've found them good for when I get restless.
Have you tried mindfulness? I've found it useful for literally everything, ESPECIALLY when restless.
I can go straight from video gaming to reading a book, but my mind takes a few minutes to adjust, and then once I'm synced up I'll tend to get restless after 15-20 minutes and look for something else to do. If I don't have anything else planned I just go back to gaming. It's pretty tough to escape this loop.