The filepaths C:\HaxeToolKit\haxe and C:\HaxeToolKit\neko both exist. I unistalled, then reinstalled haxe, then added all the filepaths to user-variables instead of system variables (as I do not have required permissions to change system variables). This worked and I was able to do haxelib run lime setup. Does this mean that lime is installed and I don't have to run lime setup windows?
EDIT: So I realized that I had added the filepath C:\Users\user\HaxeToolkit\haxe allowed me to use the haxelib command. If I follow the same format for flixel, lime, and openfl, my question now becomes, where are the commands installed to (starting from the library folder)?
Did you install the VS2015 or VS2017 build tools? I'm going to guess 2017 - it seems that Microsoft has made some changes with VS2017 and no longer sets an environment variable pointing to the c++ compiler.
Perhaps try installing the VS2015 build tools. I have had no issues targeting Windows with VS2015 installed, but my machine with VS2017 can't build for Windows.