On a (somewhat) practical note, I am wondering how far "up" he would have to go to recognize that "No, I am wrong. The horizon is visibly curved and I am actually seeing it because I am here. Therefore, my theory of a flat earth is wrong."
Now, of course, this is a "religious" matter. A matter of obsession if you will, so he will be very, very unlikely to be "converted" from his obsession. Also, the standard of disproof is much, much higher than the standard of proof. (It takes much more objective evidence to change a convicted person's mind than it takes to reinforce a conviction already present. Hysterical hysteresis if you will.)
Nevertheless, how far would you have to go to actually see a curved horizon?