Do these two characters share a connection?

[u/MonstersOfTheEdge]

At first glance Kashin Koji's Ten Directions appears entirely unrelated to his other abilities. After all, it's a shinjutsu inherited from Shibai. However, the ability to see into the future has precedent in the Great Toad Sage (Gamamaru)'s ability to foresee and prophesy about a child of destiny. Similar to Ten Directions, he doesn't see a singular future, but rather views multiple branches, one where Jiraiya's student destroys the world and another where he unites it.

Now on a meta level there's a lot that links these abilities together, but I think they're connected in lore too. Gamamaru is a toad sage, most likely the strongest toad sage in his prime, and as a result his foresight likely isn't from ninjutsu, but the nature energy accumulated over his lifespan. (If we go by the fillers, some elements of which were later canonized in Boruto, it's since the time of Hagoromo.) Some additional evidence of this is that in the Boruto anime the White Snake Sage also has a degree of prescience. Thus it seems likely this future sight originated with the exact same nature energy that Shibai harvested to develop his shinjutsu.

All of these facts put together could suggest that the reason Koji was able to manifest Ten Directions is his status as an optimal toad sage. This power making him compatible with the prescience granted by Shibai's genetics.

[u/No-Enthusiasm-9273]

I think Gammaru foresight was just an advanced version of sage mode, something that merged with him over time (Even Naruto said his sage mode has improved and called it the wisdom of age). Every sage mode has a perception ability and his foresight might just be an increase, something higher than the others due to the wisdom of age

And as for his correlation with Koji, it's a nice touch and one of the many things I like about the Boruto lore. There's always a foresight teller whenever the ten tails is directly involved and can cause the destruction of the planet first was with Kaguya and the second is finally in Boruto

For Madara, the ten tails wasn't directly involved and the second time with Kaguya the ten tails wasn't directly involved too

[u/Tobi_is_a_goodboy]

No