The rotation of the earth is not a major factor to the difference in flight times in Round earth theory. The main issue regarding the difference in flight times is headwinds and tailwinds, produced by the jet stream.
If the rotation of the earth was a factor, planes would have to travel at around 1000 miles an hour to beat the earths rotation, and even then they would just be hovering over the same spot.
everything is moving with the rotation of the earth, so any movement on the surface is always relative to the 1000 miles an hour you are already moving. When a plane is sitting on the runway, it is moving at 1000 miles an hour east, so when it takes off and flies at 500 miles an hour in the opposite direction of rotation, in reality it's net speed is 500 miles an hour towards the east, meaning that the earth is rotating underneath is. likewise, when you travel east, you are going the 1000 miles an hour that the earth is spinning plus the 500 miles an hour that the plane is flying, so your net speed is 1500 miles an hour towards the east. But because the earth is rotating under you at 1000 miles an hour, you are only going to move 500 miles an hour relative to the surface of the earth.
So all of this is to say, that in either direction, the earth's rotation is negligible because your speed relative to the earth is zero. Reading up on relativity might help you.
Another way to understand the thought experiment is to think about jumping. When you jump, the earth does not spin underneath you (relative to you) during the duration of the jump. Basket ball players do not jump further in one direction over another.