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At the end of The Last Jedi, we see some kids playing with some crude action figures and other toys before being shooed back to work in the stables by an angry Bargwill Tomder. Most of the focus has been on the young boy, Temiri Blagg, using the Force to pull his broom to himself and is pretty well covered in the question "Did the stable boy use the Force?"

The other kids that are there just before Bargwill barges in are Oniho Zaya and Arashell Sar. While the movie doesn't necessarily dedicate much time to what the three of them were doing, the novelization really helps to clarify what's going on in that small room. Oniho has set up a fairly detailed battle reenactment with the "action figures" he's crafted from discarded bits around the stables and is telling Temiri and Arashell a story about the Jedi Master Luke Skywalker and how he faced down the entire First Order by himself.

The film's editing makes it seem (at least, in my opinion) that Oniho is telling his story almost simultaneously with the events as they are taking place on Crait, or, at least, way too soon after their occurrence for news to make it to Canto Bight and the Fathier stables.

Even if this scene is supposed to take place long enough after the actual battle on Crait, it seems to me that young Oniho's story is far too detailed and accurate to be mere coincidence. Not to mention the fact that the only people who would really know the story would be the surviving Resistance fighters and the attacking First Order forces, so it seems unlikely that the story would have made it to the Canto Bight stables without being altered to either take on a more "mythical" quality by those sympathetic to the Resistance, or to down-play the battle by First Order supporters.

All of this leads me to believe that Oniho is also Force-sensitive and has the ability to "see" events around the galaxy. Like Temiri, however, I'm not certain Oniho is fully aware of the implications of such a gift, but it seems that he is taking advantage of it to tell his tales to the others.

Is there any source currently available which would confirm or deny Oniho's connection to the Force?

The main reason I see this as an "important" question is that, since it's fairly well established that Temiri is Force-sensitive, establishing that Oniho is also Force-sensitive provides us with the impression that the ability to draw upon the Force is much more common than the legends would have the galaxy believe.

It seems from the conversation between Han Solo and Rey/Finn aboard the Millenium Falcon in The Force Awakens that characters still believe that the Jedi and the Force are just myth and fairy tale. To have it shown that the connection to the Force runs deep everywhere, it could lead to a very interesting storyline with the rebirth of the Jedi (and possibly/probably the Sith).

Another related question which may be useful in this discussion is this: "How did they learn the legend of Luke?" The answers in this question include references to the novel, The Legends of Luke Skywalker, discusses how Luke was already something of a legend before the battle (something I had not taken into account), as well as some other suggestions for how the story may have reached Oniho very quickly.

As stated in the original iteration of my question, though, the one thing that still stands out is the accuracy with which Oniho seems to be relating the story. While the discussion below has given a fair amount of evidence which points to the possibility (or probability) of the young boy not being Force-sensitive, there is still no definitive or absolute proof one way or the other.

It seems that no such evidence currently exists, and it may be that we never actually get anything "official" to answer this question conclusively, but the question still remains.

You have two main reasons for why you believe Oniho is Force-sensitive and I'll try and address both points for why I believe you are mistaken.

Oniho can't possibly have known the story

This point seems to be largely discredited by Star Wars: The Last Jedi: The Visual Dictionary which states that they tell each other stories what they've heard from travellers.

As children do all across the galaxy, the stable hands engage in imaginative play to fill their downtime. Travelers from distant worlds bring them fragmented tales of adventure that excite their young imaginations.

The scene happened at a similar time to the events on Crait

Whilst I can't find anything explicit on this at the moment the following Databank page would imply that their stories come from the past and not from what they "imagine" themselves. Although it couldn't have taken place much longer after the battle on Crait because the urchins all seem to be a similar age still.

Oniho Zaya lives in the fathier stables of the Canto Casino, doing chores and trying to avoid Bargwill Tomder’s wrath. An imaginative boy, Oniho has a knack for storytelling, and entertains the other children with heroic tales set long ago and far away.

^{Star Wars, Databank, Oniho Zaya}

Lastly, I think it's also worth pointing out that in spite of any explicit evidence either way it's uncertain as to whether he is or not. Though it's more than likely that he is not Force-sensitive given what little we do know about him.

It's also worth mentioning that, that scene isn't around to introduce a new generation of Jedi, it is there to show Luke's last act has inspired hope for the Rebellion again and that he will live on as a legend. If you're interested it's worth a read of the whole interview as it's all kind of relevant but I don't really have space to add it all in.

“To me though, the big reason why, the big purpose for the kids at the end of the movie, was like you said, it’s about the influence. It’s about Luke. His whole journey through this was getting to the place where he took the mantle of Luke Skywalker: Jedi Master, the legend of that back on his shoulders, and became that legend because he realizes the galaxy needs it,” Johnson continued, as he started to relate the ending to his own experiences as a young Star Wars fan.

“The kid scene is showing that his act was about more than saving twenty lives, twenty people in a cave. That this is now going to resonate throughout the galaxy and create hope. And the fact that the kids are retelling his story, the fact that they’re being inspired by it, the fact that they’re playing with these toys that inspired me when I was a little kid playing with them, to want to grow up and have an adventure and be… I don’t know, it all ties directly back into why Luke Skywalker inspired me growing up, I suppose.”

^{IGN, Star Wars: Rian Johnson explains the ending of The Last Jedi (and the importance of toys)}

I don't see the evidence that the scene occurs very shortly after the events. It could be hours; it could be days; it could be months or more. It seems to be the intent of the scene is only to show that the story of the events on Crait did indeed spread across the galaxy and ignite a new phase of rebellion.

So the timeline certainly isn't evidence either way about the force-sensitivity of the character in question.

Bottom line: (1) it's intentionally ambiguous and (2) the force-sensitivity or not of that character isn't necessarily the purpose of that scene.

We can be pretty sure there was no galactic new network coverage, I doubt any of the First Order would have talked about that fight in that way, and the rebels were evacuating so they didn't see most of that fight. My thought is that Luke was broadcasting the fight to all Force-sensitives across the galaxy, which is what killed him not just that one projection.
We'll have to wait and see how the finale plays out but that is what I gather from the evidence in the movie.