Although in theory it sounds like an easy experiment, as others wrote, in practice it would be rather difficult. At three miles, the height of the Earth curvature in the middle is some 45 centimeters (around a foot and a half). Now you would need a perfectly flat water surface with no waves and no currents. But not only that. You would have to exclude that no garbage, fishing lines or nets, dirt, sediments, water plants, fish/plankton, or gas bubbles impact the buoyancy of your line over all the length. You would have to exclude any boat traffic in the proximity. You would have to account for the influence of the tide, atmospheric pressure difference, wind, water temperature, depth, sun exposure, evaporation rate, and vertical currents - all of that can have quite important impact on irregularities of the flatness of water body surface (look up for example the term
Atmospehric tide in WikiPedia). And even if you eliminated or accounted for all of those named effects, and measured the expected dip of ~45cm in the middle, the Flat Earth supporters would still come with some easy explanation - like for example that an Illuminati diver pulled your line to the bottom, so you would have to have cameras all over the 3 miles to prove the opposite.