The earth being flat or spherical has nothing to do with Church teaching.
The Church has never taught that the Earth was flat and although our understanding has changed throughout the ages regarding many things, Dogma and Doctrine passed down through the deposit of faith is always going to be relevant and will not and should not ever be changed.
"We do not want a Church that will move with the world, we want a Church that will move the world" - GK Chesterton