Guys I made up some nice experiments too, because what is the point in proving the earth is not spherical if we can't prove it is flat?
1 flatness in the ocean.
2 rocks.
3 Mountains.
1: We have all probably seen those nice pictures of the big and flat ocean posted around here, but, is it really flat? All you will need for this is a ruler and an ocean. Swim into the ocean, grab your ruler and put it against the water. Now, don't trick on this one, a good way to do it would be to put the ruler a few inches over and parallel to the water, now slowly move it down until it touches the ocean. Does it matches?
2: Grab a rock, is it flat? remember the rock was on the earth, if the earth was flat the rock must have at least one flat surface, the rest can be hidden underground. If you liked this experiment you can repeat it with another rock, the more the better.
3: Look at a mountain, for this experiment the mountain must be really far from you. now grab a ruler, the same ruler you took to the ocean will do, if you lost it you can use another ruler, if there are no rulers near you, grab a rock. Stand in some place where you can see the peak of the mountain, now put the ruler or the rock horizontally to the ground, if the earth is flat the mountain should be flat, slowly move the ruler or rock until it matches to the peak of the mountain, if you close one eye this will be easier. Is it flat?
There you go, have fun experimenting!