First of all, when 'land' refers to a country, we say that a person lives 'in' that land, not 'on' it.
To be honest, both 'far-away land' and 'far-flung land' are pretty much interchangeable. I should note that both are very non-specific, and are not likely to be used in a serious piece of writing.
These days, you are more likely to only hear such terms in fantasy fiction. In a serious piece of writing you are more likely to see remote places referred to as "distant lands".
There is also something quite dismissive about these terms, and I don't think that people would call a place "a far-flung land" if they could instead just name it. A common phrase that comes to mind is "the far-flung corners of the earth", which I suspect comes from the western world as it seems to suggest a starting point from which the rest of the world is measured. It could even be considered offensive to natives of a country to call it such.