That's moot because the entire ocean is in constant motion. Rotation, translation, perturbation by tidal forces. Nowhere on Earth has there ever been a flat spot in the ocean.
Lakes maybe. I am still very suspicious of the Chicago Great Lakes photo, as no one has adequately explained to me how that could be if there was a curvature in the lake. As you said, water attempts to flatten itself out. So perhaps it's that the lake water forms a flat plane connecting the two shores and there is no "horizon" on the lake because the water actually forms a straight plane between the two shores.
But with the Ocean at large, who can say. All the pictures we've seen of the Earth from far enough away come from NASA, who've been caught doctoring photos more times than I care to count.
It's clear that SOMETHING is fucky–but I don't believe we live on a flat world. Accepting that idea would require completely abandoning everything we know about cosmology and the topology of planets and star systems, and as of right now there's nothing plausible to replace it with.
Understand, I am very well-read on Flat Earth theories, and I don't believe them. There are, however, some compelling pieces of evidence which strongly suggest that our understanding of the Earth's shape IS wrong. But just how it's wrong, I couldn't say.