Doesn't look like a child's (or other amateur's) chemistry set to me. More like a very old professionals kit. It doesn't seem to be a chemistry set of an old apothecary, more like a testing kit of a geologist.
Pic 1. I see a test tube, some tubing, a thermometer (old, but not ancient) it's big in part because they need to make them big for accuracy. But at least, it's filled with alcohol, and not mercury. I don't recognize the coiled material.
Pic. 2. I see a drying tube packed with desiccant, and some porcelain crucibles.
Pic. 3. Dropping funnel, another drying tube, tongs, a flask, some filter paper. I can't really see what's in the box.
Pic. 4. Another dropping funnel, gas generating (or distilling) flask, a cork (no ground glassware here), an empty U-tube (also for drying), small flask, maybe a tube.
Nice find, anyway.