What is the explanation as to why flights take longer when flying in the direction of Earth's rotation compared to against it if the "disk" you propose is fixed and does not rotate?
I am not sure I understand this question. Flights do not take longer as you summarize. But time zones do change. My flight across times zones is the same length (assuming similar wind patterns etc) in both directions. But the time zone changes make my arrival minus departure seem shorter and longer.
As I understand, the real question underlying this would be, "Exactly how do time zones work in your flat earth theory?"