Yes and no.

It depends on what the plane speed, what direction you fly and if you are far or close to equator.

But sure, you can fly west and see continents passing below you while you stay always in daylight or night or whatever. You can easily fly as fast as the earth rotation (1000mph at equator, less and less towards the pole where it’s zero) meaning you will see the sun always at the same angle to you while they planet below you revolves.

This happens only if you fly west as you are chasing the sun going west. To land at exactly the same local time you need a very fast plane, maybe supersonic, or take a route in a northern region with a normal jet (works also south but there’s no destinations close to the South Pole to try this trick for cheap). For example Toronto-Vancouver is 5 hours of flight, and only 2 hours in local time. Meaning you lost your race with the sun but slightly, considering those 5 hours include the plane moving in the airport, you probably lost one hour out of four spent in actual flight. Similarly, London-Vancouver is 9:45 hour flight and 1:45 time difference, quite close to see the earth rotate below you while not moving relative to the sun.

You just need to match the earth rotation speed in your area. Which again can be between 1000 and zero mph. Altho standing still in the North Pole is a bit of a cheat.