I wrote this small guide so other people might benefit from my experiences. Feel free to leave a comment if you have any questions or remarks. First a quick introduction:

haXe is a high-level object-oriented programming language mainly focused on helping programers develop Websites and Web applications. haXe has been designed to be easily portable across several platforms.
source: haxe.org

I downloaded the Linux installer and also the HaXe 1.18 for Linux and Neko VM 1.70 zipped files into one directory. Then started a terminal and navigated to this directory and started the installer:

sudo ./hxinst-linux

This launched the GUI installer, which used my previous downloaded zipped versions of HaXe and Neko instead of downloading them again. Nice! I closed the window after the installer finished and typed in the terminal:

haxe

This resulted in a long list of options possible with haxe. Installation succeeded! Next: install swfmill