The game will define the flag in your profile according to your device's language or region. To change your flag you must either change your device's language or region. This process can vary according to your device's platform:

iOS Device
  1. Open your device's Settings
  2. Go to General, then click on Language and Region
  3. Select the desired country corresponding to the flag you would like to use

Android Device
  1. Open your device's Settings
  2. Search for "Language" or "Region". The options may be different depending on the device model and version
  3. Select the desired country corresponding to the flag you would like to use

The changes should take effect when you reopen the game.