The library is compiled using MSVC so it can not be liked to your application with a MinGW compiler. You can get the code from Here and compile it with MinGW compiler. After that you can link it to your app.
You can download and install CMake from Here. Next open the file named "CMakeLists.txt" from the root of the VLC_Qt source code with Qt Creator. Click "Next" and then after selecting the desired Generator click "Run CMake". WHen everything completes click finish. Now you can build the entire VLC-Qt with Qt Creator.