If you only need a bit, there is often a layer of clay silt underneath the sand in the
water on a shallow lake beach. As a kid, I LOVED diving for it, digging it out, and making mud figurines. Might not be ideal for pottery.
Otherwise - most soil (unless specifically manufactured and cleaned) has SOME clay- even if only 3-5%. For your purposes, you could make a small grizzly - basically a screen on an angle. You dump dryish soil slowly onto it. Stuff that is smaller than the screen (maybe use hardware cloth?) Falls through. The gravel bounces off to the side and makes a pile that can be used for other projects. This would give you maybe 10-20% clay, depending on what percent gravel you had. 20% clay is more than
enough to exhibit clay-ey properties.
You can buy bags of bentonite chips or ground bentonite. They are clay, but a special expansive super slime clay. Kids would have fun with bentonite, but it's not really representative of most clay.
I think your kids are still too young, but you can do some great science/math problems with a scale and some different sized sieves (if they are doing algebra already- let me know and I will give you ideas)