I created this account just to ask this question because I couldn't find it anywhere else, but in the moving diagram on the societies website (I have attached a screenshot and a link to the page due to restrictions on attachment size) - which the wiki says is the generally most accepted model for the movement of the sun and the moon - it doesn't explain the lunar cycle (New moon, waxing, full moon, waning). In normal science it is explained with the shadow of the round earth being cast onto the light side of the moon, however this can not be the case if the earth is flat and the light side of the moon never passes through the shadow of the earth, or any shadow for that instance. In this model the bottom of the moon would be more cut off starting from half way the further away from the north pole you are due to only the side facing the sun being lit up and the bottom not (unless the sun is significantly closer to the earth than the moon). Further more, through out the night the angle of the cut off the bottom of the moon would also change due to the angle at which you would view the moon and to a more severe degree again depending on your distance from the north pole (I don't want to say latitude as that relies on the degree around the earth you are and that clearly has no relevance to a flat earth). Please can someone explain this.
https://wiki.tfes.org/Frequently_Asked_Questions - link to moving diagram of day night cycle