Is there a way to know which Android API version is my flutter app using?

You can use device_info package:

DeviceInfoPlugin deviceInfoPlugin = DeviceInfoPlugin();
final androidInfo = await deviceInfoPlugin.androidInfo;
return androidInfo.version.sdkInt;

Open your android build.gradle (Module:app) and there you can see :

minSdkVersion

targetSdkVersion

compileSdkVersion etc.