Is there a good experiment to demonstrate Gauss's Law for Magnetism?

If I understood your question correctly, then you want a simple experiment to demonstrate that magnetic monopoles cannot exist. The simplest way to explain this to a high schooler would be to actually break a small piece of magnet, and then make the student realize that the poles of the magnet haven't been 'split'; instead, both the pieces contain two poles.

I can't think of anything simpler than this and I have myself used this experiment to explain the concept of magnetic monopoles. Maybe some of the more knowledgeable folks here can help you out.