When it comes to the timeline, Breath of the Wild does not seem to be a direct sequel to any of the other games, like Twilight Princess or Wind Waker. It stands apart from pretty much every other game in the series. However, there is evidence for a very different timeline placement. To find out what it is, several pieces of evidence must be examined.
The locations in the game are big pointers. Here are some important ones. Mekar Island is by the Lost Woods. This is spelled differently than Makar, but over time, such errors could develop. On the island itself, there is a twisted, rotted tree. If you go to the top of the tree, the whistling wind sounds like Makar's Song. This seems to point towards the Adult Era Timeline. This is further supported by a few more things.
Have you ever considered the names of the Divine Beasts? Their names are Vah Ruta, Vah Medoh, Vah Rudania, and Vah Naboris. These seem like just some names that they came up with, but in reality, they are much more important.
Ruta, Rudania, and Naboris are named after the sages Ruto, Darunia, and Nabooru, from Ocarina of Time. Since this game is consistent across all three timelines, these are not important. What is important is Medoh. It is named after Rito Sage Medli, who only appears in the Adult Era Timeline.
The final piece of evidence for the Adult Era is salt. Rock Salt. The item description is "Crystallized salt from the ancient sea, commonly used to season meals. Cannot be eaten in this form". The key here is Ancient Sea. This could be referring to the Great Sea from Wind Waker.
So overall, there seems to be a lot of evidence for the Adult Era, and this would be great if that was all the evidence for the timeline placement. However, there is evidence for the other two timelines. Let's start with the Child Era.
The Child Era timeline does not have much evidence, but the one piece of evidence is massive. At the knighting ceremony, when Link is knighted by Zelda while the four champions watch, she says something intriguing. "Whether skyward bound, adrift in time, or steeped in the glowing embers of twilight, the sword is forever bound to the soul of the hero". "skyward bound" and "adrift in time" both refer to Skyward Sword and Ocarina of Time, which are before the timeline split. But "steeped in the glowing embers of twilight" is referring to Twilight Princess. This game is only in the Child Era timeline.
But that is where the evidence for the Child Era ends. And frankly, it doesn't seem like a lot to go off of. This leaves one other timeline. What evidence is there for the Hero is Defeated timeline?
There is some evidence for this timeline. First, there are some locations that are seen only in the failed hero timeline. Spectacle Rock, a particular rock formation that looks like a pair of spectacles, is one of those locations (if you want to see it, the Gerudo Desert Tower is on one spectacle, and Vah Naboris rests on the other spectacle after completing it).
Also, Ganon is evidence. You probably have noticed that you do not ever see Ganon's Gerudo form, Ganondorf, in Breath of the Wild. You also never see Ganondorf in any of the games falling into the failed hero timeline. And this is official. Hyrule Historia says that one Ganon defeated Link in Ocarina of Time, he shed his Gerudo form to become the incarnation of evil, Ganon.
All this evidence for all three timelines might leave you confused. There seems to be evidence for all three timelines. That is why my view of Breath of the Wild's timeline placement is that all the timelines converge into Breath of the Wild, finally unifying the Zelda timeline. Tell me any problems you may have with this, or your own views.