Alrighty, flat Earthers. I have a challenge for you....Start where you're at, and move east. Keep moving east until you arrive at your starting point. Then explain to me why you were able to do that if the earth is flat.
I'm not a FE, but I can show you why your proposed experiment does not prove either side. You want to move East, always East, right? How are you determining your direction? Several methods appear viable, and all can be shown to be insufficient to prove RE or FE.
1. Magnetic compass? On the FE model of the earth, the compass always points North to the center of the disk. If you are far enough away from that spot, your path will LOOK and FEEL like a straight line, but will turn in a very gradual circle, imperceptible to you, that curves you back to your starting point. For that matter, as pointed out by others, the illustration can be done if you are very close to the pole, in which case the FE and RE models produce the exact same result.
2. The motion of the Sun? Here again, FE has an answer that your observations will not be able to disprove: their Sun does not behave the way you know it to, but instead follows a circular path in the sky. Once again, the path you take toward sunrise / away from sunset will appear straight to you, but will not be.
3. GPS? Here you have several problems, not least of which is that you are no longer making your own determination of direction but instead are counting on someone else. This opens you up to manipulation by agents of the supposed RE conspiracy to trick you into seeing evidence that they want you to see, confirming your belief in the RE world.
In cases 1 and 2 (and possibly case 3 but who's to say), both the RE and the FE models have you taking a curved path; the two models simply disagree on the direction of that curvature. RE have you turning down, down, down, going more or less 'upside down' from your starting point when you are halfway home, then more down, down, down until you have returned upright at the start. FE have you turning left, left, left, all the way around a flat track.