Whenever I come across situation to make someone believes in something, I try to become that person so that I understand their perspective to design a way that will change their mind. 
So I am far from flat earther but if I were this is how I prove it.
Using basic geometry calculation and experiment we can determine that earth is flat or curved. 
Let us station two points at sea level (p1 and p2) which are very far apart and let name the distance between them as “b”. At both p1 and p2 we install retroreflector sensor that can read retroreflector stationed in the moon. Since a moon can appear directly overhead to earth on specific location on earth equator, we can place p1 at a point where the earth sensor is 90 degrees to the tangent of the sea level surface at that point.  When you read the distance from point p1 to the moon retroreflector which we name is as “a”, it will be constant (360,000 Km when the moon is closest to earth). At the same time and using the same moon retroreflector you will measure the distance from point p2 to the moon retroreflector which we can name is as “c”, you will get a value greater that the reading from p1 which is “b”. 
If a2+b2=c2 , then the earth is flat but if the reading c is greater that the c from the calculation the eath surface I is curved.