Learn English – Usage of the word “unlike”

In standard English usage, fellow is neutral and informal, as Jim notes in his comment. It would be appropriate for relaxed gatherings. Think of a speaker at a technology conference, for instance:

"And I tell you, this fellow right here, he is an inspiration to all of us."

It would also be appropriate at parties. Think of the song:

"For he's a jolly good fellow."

On the other hand, it can be used negatively as appropriate. In these contexts it would indicate derision or intensity.

"Nasty fellow, always coming up with some new scheme for getting his own money with other peoples' effort."

"I won't deny, he works like a horse, but nice? No, he's definitely not a nice fellow."

The use of the word should be a deliberate choice if the context is not completely casual. In a small group of friends having drinks together, it's pretty much always appropriate. A speaker might use it to help loosen up his audience, as in the first sentence I noted. Using it in writing is inadvisable unless the context specfically calls for informality and a folksy feel. A find/replace from person to fellow is not a safe or good idea.

My gut feeling aligns with yours – it sounds off to me. I did some research on Google that seems to confirm our hunches.

One reason it sounds off, I think, is because kid and boy both connote a young age. So, the phrase sounds redundant. You could simply say:

There was a boy hurling stones at a cute puppy.

or:

There was a kid hurling stones at a cute puppy.

I suppose one could argue that a "boy" could be an adoloscent, so, some clarification about age might be in order. However, if you wanted to clarify, you could say:

There was a young boy hurling stones at a cute puppy.

Ngrams found plenty of hits for "a young boy" and "a young girl," but came back empty-handed for "a kid boy" and "a kid girl".

I found several hits on Google for "a kid boy", but they were excellent examples of why hit counts need to be examined carefully. Many of them had extra punctuation, like this:

If you had a kid, boy or girl, and wanted to know...

Some even used the word boy as an exclamation, like this Pinterest tag:

Pins about: Toys I had as a kid. Boy I miss them!

There were several hits that were labels to stock illustrations:

Illustration of a Kid Boy Dressed as Prince Sitting on a Student Chair

but redundancy makes sense in that context, because those who title images in an image database want customers to get hits if they search for boy or search for kid.

But I'd avoid it in a context like the one you are asking about.