I'll agree with others that "flip-flop" probably does not convey the idea you want. Yes, if I heard "Flip-Flop Nation", my first thought would be, "country of people who change their minds constantly". Next thought would be "country of people who wear sandals". If told neither of these were correct, I might think of SF's definition and say "country where electronic logic circuits are fabricated".
Perhaps you need to clarify what you DO want to say. Are you trying to say "nation of people who travel a lot"? "Nation of people who know a lot about other cultures"? Literal phrases would be "Travelling Nation", "Well-travelled nation", "Wandering Nation", "Mobile Nation", "Culturally-Aware Nation", "Culturally-Sensitive Nation", "Global Nation", "Nation of World Learners", etc, though none of those are particularly clever or catchy and most or all are subject to alternative interpretations. I'm not sure if you consider "nation" an essential part of the phrase. Perhaps something more along the lines of "Global Travellers", "Culture Travellers", "International Awareness", etc etc.