You complain "stop messing this thread up with discussions about the south pole".
Last I heard the south pole was in the southern hemisphere and the thread is: "How can the sun be seen more than 12 hours a day in the southern hemisphere?"
No offense, I was referring to the upcoming discussions about Scott and Amundsen, the magnetic field lines, etc.
For the sake of the qualitiy of this thread I suggest to stick to the topic of day, night and daylength as it can be observed at different places around the earth and how this is (or is not) compatible to the Flat Earth model.
So... Can I assume that I just debunked the flat earth theory? 
Is nobody here able to properly explain to me how it is possible on a flat earth to see the sun in South America and Australia
Why are you so sure you can? They are on opposite sides of the earth on a round earth too. The charts seem to suggest you made up that you can see the sun in both places at once.
How do you know you can see the sun in both places at once? Have you tested it yourself, or were you told that?
The sun can be seen at Australia and South America at the same time because of the axial tilt of the globe.
Unfortunately I am not able to be at both of those places at once, therefore testing it by myself seems quite impossible for me...
Fortunately we live in the 21st century and we can do something called research, in order to gather information we can't test ourselfes. Please notice that doing research is completely different from "beeing told" something.
First of all, my example takes place at every day from a few weeks before the 22 December till a few weeks after, every year, at 09:00:00 (UTC time).
timeanddate.com provides a interactive woldmap with which you can observe, where on the world it is day and where it is night for every moment you can think of:
http://www.timeanddate.com/worldclock/sunearth.htmltimeanddate.com is a private company. Providing false data (especially predictions of day and night) would soon be noticed by the user community and they would use other websites, which provide the correct data. Users are money and a lack of users is a lack of money. timeanddate.com would vanish. Because this didn't happen I am quite convinced that timeanddate.com provides correct data.
I went even further: I validated the correctness of the map by myself, by observing several webcams all over the world (
http://www.earthcam.com/), and I encourage you to do so as well. I was not able to detect any deviation between the day/night prediction of the map, and the daytime, seen in the webcams. Another reason, why the maps, provided by timeanddate.com seem valid to me.