We're basically being threatened with being attacked and are being held against our will unless we agree to do as they say.
I see the choices here as basically a "Fight", "Run", "Give up freedom" or "Pretend to give up freedom and then Fight". From those choices I have a pretty good idea of what Flan (a girl who's extremely impulsive, used to be on top of the food chain (or atleast near the top), and doesn't care at all for people she doesn't like or respect as strong) would go for. Even if she loses (and that's very much a big if), that'll only make it in character for her to possibly listen to them more now that they've proved they're not weaklings. Besides Flandre LIKES to fight, and strong opponents too. So for her it's a win/win; either Fight Strong Opponents, or Destroy weaklings trying to control you. Besides she's here on Vacation for fun, why the hell should she listen to and follow the rules of people she just met and are trying to intimidate her? They're just snacks. They need to be taught their place (food, and below her).