If you flew a fighter jet, equal to the rotation speed of earth, in the opposite direction of the rotation of earth, what would happen?

I would be arrested for flying a plane without a licence and for stealing a fighter jet from the air force. I probably would spend a few years in prison. I might even be sued for damages.

All that however would depend on whether I could safely land or whether I did an MH340 disappearing without trace.

You might get back in time to see yourself take off.

A thousand miles an hour (approximate speed of ground surface at the equator) is not a big deal. Now, we do have the issue of what we mean by speed if the plane. Is it 1000 mph from an outside perspective or 1000 mph relative to ground? In essence, if you were to travel at the same speed as the underlying earth, but in the opposite direction, you would appear to be not moving from the outside. You would maintain a position on a line between the center of the earth and whatever object was directly overhead. From the outside, you would be immobile.

nothing/

i'm sure that's the definition of orbiting

nothing will happen, you fly to your destination normally, this has been done many times. But at the equator, you will keep pace with the earth's rotation, so the sun will appear suspended in the sky.

You can get this effect in an ordinary jet at higher latitudes, as the rotation rate is slower there. You can see this, the sun stationary in the sky, in a commercial airliner.

Remember velocity is relative.

You would only be traveling at 1.3 times the speed of sound if at the equator.

The speed of sound is about 1225 km/h while the Earth spins at 1600 km/h at the equator.

The further away from the equator, the slower the plane needs to fly. And depending on your aircraft, the closer to the poles, the closer your plane won't maintain alitiude because it's travelling too slow.

At the equator, the speed of rotation of the Earth is very roughly 1,000 mph. A plane flying West at that speed would arrive at the same time it left. A plane flying East at that speed would arrive 2 hours later for every hour it flew. Concorde flying from Paris to Caracas arrived at the same time it took off. Flying back, it arrived 12 hours after it took off.

no

I would travel back in time to the day before you were born and have the chance to kill your parents like Terminator to prevent you from being born and prevent your question from ever being posted.