Theoretically, you’d find the sunset point, and simply counter the speed of the earth’s spin around that point. But with the earth’s axis at 23.5 degrees, even at the equator, there will be small seasonal variations.
The closer you are to the equator, the more even the days are, regardless of the season. The equator is 0. This is the longest latitudinal line on the planet, so it would take the longest to get around. The speed at which the earth spins varies upon your latitudinal location on the planet. If you’re standing at the north pole, the speed is almost zero but at the equator, where the circumference of the earth is greatest, the speed is about 1,038 miles per hour (1,670 kph). But, helicopters can’t fly that fast, so you’d have to choose a higher latitude to follow….....but even the mid latitudes spin at 700 to 900 mph (1125 to 1450 kph), so you’d be stuck in the higher latitudes, where seasonal fluctuations are most dramatic.
‘Helicopters by their nature tend to be much less efficient long-range vehicles than fixed-wing aircraft. As a result, the record for maximum range is far lower and there has been little effort to break it for decades. The current official record belongs to Robert Ferry who flew a prototype YOH-6 Cayuse on a cross-country flight from California to Florida on 6 April 1966. The distance covered on the journey was 1,923.08 nm (3,561.55 km).’
Fixed wing aircraft might be a better option perhaps, for both speed and distance.