No. We've known for thousands of years, in fact, that the Earth is not flat. There are several clues that can prove this. First, looking up at the night sky, we cannot see every star or constellation at the same time, indicating that we rotate out of view of certain stars (Aristotle, 350 BCE). Several ancient Greeks, Cleomedes and Eratosthenes, not only figured out the Earth was round, but were able to get a decent approximation of Earth's circumference not long after Aristotle made his observation. Beyond that, there are many other indicators:
Visibility of distant objects falling below the horizon
Lunar eclipses and the appearance of the Moon
Observations of the Sun and fixed stars and constellations
Circumnavigating the surface of the globe (returning to the same place if traveling in the same direction)
Distortion of grid based systems based on latitude
Weather patterns (Coriolis, differential temperatures and climate between poles and equator)
Gravity (could not work without a spherical body)
Observations from aircraft, spacecraft
Ultimately there are many lines of evidence that point to a flat earth, and those who insist the Earth is flat are lost in a world of conspiracy theory.
A representation of how Cleomedes calculated the Earth's circumference, by measuring shadows at different points on the same day of the year.
Another very real image of the round Earth from the Moon.