Все получилось! 

procedure TForm1.Button1Click(Sender: TObject);
var
  stringstream: TStringStream;
begin
  stringstream:=TStringStream.Create('');
  try
    IdHTTP1.Request.ContentEncoding := 'utf-8';
    IdHTTP1.Request.ContentType:='application/xml';
    IdHTTP1.Request.Accept:='application/xml';
    IdHTTP1.Request.CustomHeaders.Add('Authorization: Token ***');
    stringstream.WriteString(UTF8Encode('<req><query>Киров</query></req>'));

    Memo1.Text:=IdHTTP1.Post('http://suggestions.dadata.ru/suggestions/api/4_1/rs/suggest/address', stringstream);
    Memo1.Text :=Utf8ToAnsi(Memo1.Text)
  finally
    stringstream.Free;
  end;
end;

end.