This question is fairly old at this point but for anyone in the future wondering how I solved it, I ended up switching compilers to Clang and creating a .bat file the just runs clang++ and links the SFML lib directory. (SFML GCC-64 worked fine with Clang)
To fix any errors in VS Code, you can add SFML to the workspace config
in .vscode/c_cpp_properties.json:
add or edit a field called "configurations" (should be an array), and add the following:
    "configurations": [
      {
        "name": "SFML",
        "intelliSenseMode": "clang-x64",
        "includePath": ["${defaultInclude}", "C:/libs/SFML/GCC-64-Bit/SFML-2.5.1/include"],
        "compilerPath": "C:/msys64/mingw64/bin/clang++.exe",
        "cStandard": "c11",
        "cppStandard": "c++17",
        "browse": {
          "path": ["${workspaceFolder}"],
          "limitSymbolsToIncludedHeaders": true,
          "databaseFilename": ""
        }
      }
    ]
You'll have to change some of the paths to fit your setup, and you could very well put this in your global C++ configuration.
Finally, make sure that the needed DLLs are copied to your compilation output directory