Remember, Boruto is part Hyuga and now 80% Ōtsutsuki. Both the Ōtsutsuki Clan and the Hyuga Clan can awaken the Byakugan. As Boruto’s body rapidly becomes less of himself and more Momoshiki, he should also have access to a Byakugan, as his body transforms.
Again, this is all confirmed through canon content, which clearly showcases Boruto having a Byakugan. In addition, the same logic should apply to the Rinnegan of the Rine Sharingan. Momoshiki has Rinnegan abilities and as Boruto’s body starts to transform into Momoshiki, he too should have access to these abilities.
Thus far, Boruto doesn’t seem to be aware of all of this and has only just started to theorize with Kawaki about being able to perform Ōtsutsuki techniques such as Karma. However, if Boruto can use Karma and is a Byakugan can manifest due to Momoshiki’s cells slowly taking over, then a Rinnegan should also be possible, as should Boruto’s access to these powers also be possible.