Question: How is "conjunction" possible on a flat earth?
Answer: The luni-solar conjunction is no different on the flat earth than it is on the globe. "Conjunction" simply means "the action or an instance of two or more events or things occurring at the same point in time or space." The sun, because of its slightly faster motion, pulls ahead of the moon by about 12.2° each day. Consequently, it gets so far ahead of the moon that it circles around behind it and overtakes it again after about 29.5 days (12.2° x 29.5 = 360° = a full circle). The luni-solar conjunction is the precise moment in time when the sun is again in line with the moon (the same celestial longitude) before it once again moves ahead of the moon at the beginning of the next lunar cycle. The time of conjunction is often referred to as the astronomical "new moon."
The following video roughly illustrates what happens during the first 24-hours after conjunction on the flat earth: https://www.youtube.com/watch?
You can find a list of conjunction times (UTC) here: http://aa.usno.navy.mil/data/d