minSdkVersion

It is indeed possible to increase minSdkVersion, but it took me way too much time to find it out because google searches mostly yields as result discussions about the absolute minimum Sdk version flutter should be able to support, not how to increase it in your own project.

Like in an Android Studio project, you have to edit the build.gradlefile. In a flutter project, it is found at the path ./android/app/build.gradle.

The parameter that needs to be changed is, of course, minSdkVersion 16, bumping it up to what you need (in this case 19).

defaultConfig {
    // TODO: Specify your own unique Application ID (https://developer.android.com/studio/build/application-id.html).
    applicationId "com.example.projectname"
    minSdkVersion 19 //*** This is the part that needs to be changed, previously was 16
    targetSdkVersion 28
    versionCode 1
    versionName "1.0"
    testInstrumentationRunner "android.support.test.runner.AndroidJUnitRunner"
}

Seems obvious now, but took me long enough to figure it out on my own.

defaultConfig {
    // TODO: Specify your own unique Application ID (https://developer.android.com/studio/build/application-id.html).
    applicationId "com.example.projectname"
    minSdkVersion 16 // <--- There
    targetSdkVersion 27
    versionCode 1
    versionName "1.0"
    testInstrumentationRunner "android.support.test.runner.AndroidJUnitRunner"
}