Well we can focus on the Child Timeline while referencing the other two at different points by the Sheikah tribe members and Impa who are tasked to help protect Link, Zelda, Arceus, and Blackfire from within the shadows. I have a headcanon that Impa and the Sheikah tribe are aware of the existance of two other Hyrules in different timelines. Now lets continue the story and how will we do Blackfire if she is alive? Captured maybe?
I sent you chapter one and I am thinking that since Blackfire in me and Alexs fanfic remained alive since Link and Zelda directly intervened in the battle this would be the Child Timeline. Of course the other two timelines have a different outcome with the Adult Timeline Arceus and Blackfire are both killed while in the Downfall Timeline only Arceus of that timeline lived. Since in the Downfall Timeline the Hero of Time was killed by Ganon who claimed the entire Triforce, was able to spread his malice into the Pokemon World which was a peace after the battle. However, since this Pokemon World did not have Mega Evolution and the Kalos war never happened along with it being the world of gen one to four, it was ravaged by Ultra Beasts as well.
We may need to retcon Blackfire being dead but what would she be doing at this time if Link and Zelda already saved both of them before possibly before the events of the Jewel of Life. I think Zelda already sealed Darkstar in the same way Hylia sealed Demise with Link splitting the soul in fragments and sealing the evil across time in different eras of Hyrule. The Link and Zelda that did this would be the most recent incarnations before the current Link and Zelda who like all incarnations are bound together as a couple by Hylias blessing.