First off, I think people shouldn't put too much stock in any timeline theory just yet. Nintendo has a history of building upon ideas from previous Zelda games without much regard to the timeline before. There are also plenty of examples of significant contradictions within the timeline.
That being said, if we are going to discuss the timeline, we might as well have fun with it.
Now, this Zelda game clearly takes place in a later part of the timeline after Hyrule became large and prosperous and then suffered a significant decline. The first thing that comes to mind is of course the era of the original Zelda and The Adventure of Link. The Adventure of Link is one of the few Zelda games that features a world comparable in size to the one we are seeing in Breath of the Wild. Even if Breath of the Wild takes place in a different part of the timeline, I wouldn't be surprised to see a few locations from The Adventure of Link be present in the new game.
Alternatively, Breath of the Wild could take place in the same timeline as Twilight Princess, in some equivalent spot to Zelda 1 or 2.
Now, Breath of the Wild could be in the Wind Waker timeline, but I find it doubtful. It it was, it would have to take place before the Great Sea is created, serving as a prequel to Wind Waker. After all, Hyrule is abandoned and destroyed at the end of Wind Waker, and the Hylian people instead move to a new land and make a home for themselves there. I find that less likely, since it would probably result in Breath of the Wild creating big contradictions with Wind Waker.
Finally, there is a fourth option: a whole new branch of the timeline. In this theory, a new branch of the timeline was created based on the ending of Skyward Sword, which had similar conditions to the timeline branching seen in Ocarina of Time. In order to lead to Breath of the Wilds, this timeline would have needed to follow a similar trajectory to the timelines we are familiar with, perhaps implausibly so. However, it might help explain why there is so much Sheikah super-tech present in Breath of the Wild that isn't seen in games outside of Skyward Sword.