You must add next code. Devices have Android 6.0 or later.
if(ContextCompat.checkSelfPermission(this, Manifest.permission.WRITE_EXTERNAL_STORAGE) == PackageManager.PERMISSION_GRANTED){
        Intent intent = new Intent(MediaStore.ACTION_VIDEO_CAPTURE);
        startActivityForResult(intent, 1);
    } else {
        ActivityCompat.requestPermissions(this, new String[]{Manifest.permission.WRITE_EXTERNAL_STORAGE}, 2);
    }
If your the app has the permission for use the STORAGE we open the STORAGE.
If your the app doesn't have permission for use STORAGE, we open system-dialog.
Result from the dialog you can see in the onRequestPermissionsResult. (You must override it on your Activity).
@Override
public void onRequestPermissionsResult(int requestCode, @NonNull String[] permissions,
        @NonNull int[] grantResults) {
    if (requestCode == 2) {
        if (grantResults.length > 0 && grantResults[0] == PackageManager.PERMISSION_GRANTED) {
            Intent intent = new Intent(MediaStore.ACTION_VIDEO_CAPTURE);
            startActivityForResult(intent, 1);
        }
    }
}
I think you must extract next lines to the private method.
private void takePhoto() {
    Intent intent = new Intent(MediaStore.ACTION_VIDEO_CAPTURE);
    startActivityForResult(intent, 1);
}
For more information see : https://developer.android.com/training/permissions/requesting.html