Learn English – May I use the word ‘vacational’ (as opposed to vocational)

Significant means meaningful; it says nothing about magnitude. A small advance may be significant:

Gene analysis based on work done by the publicly funded Human Genome Project may have moved science a small but significant step closer to finding a better treatment for Alzheimer's disease.

By the same token, a large advance may be insignificant:

This tonnage represent a very large advance in airborne volume, but is still insignificant relative to over-the-road volume.

So if you mean significant, write significant - don't replace it with big or large or huge. If however you are talking about magnitude, let usage guide you; consulting a corpus is a very good idea. (But at the BYU site you want COCA, Corpus of Contemporary American Usage, or BNC, British National Corpus, rather than COHA.) Large and big vary idiomatically; huge, however, signifies a much greater magnitude than either of those, amazingly large, and in formal usage will suggest you are speaking hyperbolically unless you can substantiate the choice.

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.