I think Hinata will meet Kaguya, just as Naruto and Sasuke met Hagoromo. I believe this because Hinata too lost consciousness like Naruto and sasuke back in chapter 662. And all three happened one after another. First Naruto, shortly after it was sasuke, and then Hinata.
And lets be honest, Hinata fainting over a trip is pretty unrealistic and dumb, unless of course, it was for the sake of plot, as in, meeting Kaguya.
For those who don't believe she actually lost consciousness:
There’s also the fact that Kaguya would be the perfect character to reveal the long awaited history of not only the hyuga but also the uzumaki clan, seeing her connection to the Byakugan and Uzumaki’s RDS. She could explain the creation of the cursed seal, jyuuken, the RDS, fuinjutsu, and other things related to the hyuga and uzumaki.
Hell, considering how she was a power hungry woman, it would make sense for her to have been the one who would exploit the Byakugan’s eye powers and chakra control enhancements and create jyuuken herself. she would use the eye to its full potential Kishimoto did say some time ago that we would he getting hyuga clan development and it seems that the revelation of Kaguya having Byakugan is the beginning of this development. Hinata being part of this development seems only logical considering she’s the only relevant hyuga character left around.
There are also some similarities between Hinata and Kaguya
•Byakugan
•Females
•Heiresses
•Leaders
•Stoic and Quite
•Hime-style hair cut
• creepy (lol jk)
There is however, a difference in their ideologies in that, as neji once said, Hinata wishes for harmony and peace by avoiding using power and kindness instead (much like Naruto and ashura) while Kaguya believes in using force and power to bring peace even if that means ridding herself of kindness (like indra and Madara). I think this will play a role in the sense that Kaguya will regret what happened to her and would want Hinata, her successor, to correct this.
Considering Kaguya is a mother, and how kishi has this trope of mothers being scary yet caring (ex: kushina), I wouldn’t put it past him to show us a more caring side of Kaguya; because at this point, we’ve only heard about her darkness. And considering villains like Neji, sasuke and nagato, kishi isn't one to paint his villains all in one color, so I think we'll see a more caring and motherly side to Kaguya.
To add to the supporting evidence that Kaguya will meet Hinata;
We still don't know why hagoromo implied he was an alien.
We still don't know where Kaguya came from.
We still don't know what the significance of introducing a 2nd sage was.
We still don't know if the Byakugan is kaguya's natural eye.
We still don't know how the hyuga clan formed.
We still don't know how the uzumaki clan formed.
We still don't know the relation between Kaguya and the shinigami.
We still don't know why Kaguya didn't fight juubi herself.
We still don't know how kaguya's ET came to an end.
We still don't know the relation between hagoromo, his brother, and Kaguya.
We still don't know the origins of the rennigan (was hagoromo born with it or did it mutate?)
We still don't know what the "secrets of the Byakugan" are.
most of these unanswered questions relate to kaguya/the hyuga and the byakugan, and since kishi already said wed get hyuga clan development, i think it makes sense for kaguya to explain the history of the byakugan and htyga to hinata.
Add all This to what I said, and its very clear that Kaguya will be the one to explain all this to someone
and Hinata is the perfect and only option