Flexibility means being able to change your approach depending on the situation. Response means how you react to something that happens. So flexible response means being able to change the way you react depending on what is happening.
Think about playing a game of rock-paper-scissors. If you always choose rock, your response is not very flexible. But if you change your choice every time, depending on what your opponent chooses, you are using a flexible response.
In the real world, countries have different ways to respond to threats or conflicts. One way to respond to a conflict is to use military force right away. But flexible response means having different options to respond, not just jumping to a military solution.
For example, if another country is being aggressive, instead of just starting a war, a country could start by sending a warning or sanction. If that doesn't do the trick, then the country could use military force as a last resort, but only as a necessary measure.
So, flexible response is about having different ways of reacting to a situation, and choosing the right response based on the situation.