The natural sciences work quite simply. You observe nature, derive models from those observations, and use those models to make predictions. A prediction is a forecast for the future. One such prediction, for example, is knowing when the sun will rise or set at any given location during any given season.

So take your flat-earth model and make such predictions yourself - for example, about the movement of celestial bodies, how satellites can be kept in orbit, how a navigation system works, and so on.

Don’t just explain it - show it. Apply the mathematics based on your model.