Environment variables in Linux are supported now in VSCode (although I don't know since when or which version exactly). I have VSCode for Linux 1.73.1.

You can now use the following (just like in the question above):

{
    "java.home": "${env:HOME}/.sdkman/candidates/java/8.0.222.hs-adpt/"
}

Here is an example, you set the value in the environment block.

    {
// Use IntelliSense to learn about possible attributes.
// Hover to view descriptions of existing attributes.
// For more information, visit: https://go.microsoft.com/fwlink/?linkid=830387
"version": "0.2.0",
"configurations": [
    {
        "name": "g++ - (GDB 9.2) Build and debug active file with RepoCodeInspection",
        "type": "cppdbg",
        "request": "launch",
        "program": "${fileDirname}/bin/${fileBasenameNoExtension}",
        "args": [],
        "stopAtEntry": false,
        "cwd": "${workspaceFolder}",
        "environment": [
            {
                "description": "same as commands below by using 'setenv ...",
                "info": "cant debug b/c of libBase/libRecipe now requiring dependency to boost for stacktrace dumps",
                "name": "LD_LIBRARY_PATH",
                "value": "/libs/:./"
            }
        ],
        "externalConsole": false,
        "MIMode": "gdb",
        "setupCommands": [
            {
                "description": "Enable pretty-printing for gdb",
                "text": "-enable-pretty-printing",
                "ignoreFailures": true
            }
        ],
        "logging": {
            "trace": false,
            "traceResponse": false
        },
        "preLaunchTask": "RepoCodeInspection",
        
    },
    {
        "name": "g++ - (GDB 9.2) Attach to a running process",
        "type": "cppdbg",
        "request": "attach",
        "processId":"${command:pickProcess}",
        "program": "${fileDirname}/bin/${fileBasenameNoExtension}",
        "MIMode": "gdb",
        "setupCommands": [
            {
                "description": "Enable pretty-printing for gdb",
                "text": "-enable-pretty-printing",
                "ignoreFailures": true
            }
        ],
        "logging": {
            "trace": false,
            "traceResponse": false
        },
        "preLaunchTask": "RepoCodeInspection",
       
    },
]

}

Despite that this is an older question, for the sake of completeness: This now works with version 1.79.0 (maybe also earlier) of VS code. At least I was able to successfully use ${env:USERPROFILE) in the settings.json file, running VSC at Windows 10. This seems to be case-insensitive, UserProfile did work, too.

Assuming you mean for a debugging session(?) then you can include a env property in your launch configuration.

If you open the .vscode/launch.json file in your workspace or select Debug > Open Configurations then you should see a set of launch configurations for debugging your code. You can then add to it an env property with a dictionary of string:string.

Here is an example for an ASP.NET Core app from their standard web template setting the ASPNETCORE_ENVIRONMENT to Development :

{
  "version": "0.2.0",
  "configurations": [
    {
      "name": ".NET Core Launch (web)",
      "type": "coreclr",
      "request": "launch",
      "preLaunchTask": "build",
      // If you have changed target frameworks, make sure to update the program path.
      "program": "${workspaceFolder}/bin/Debug/netcoreapp2.0/vscode-env.dll",
      "args": [],
      "cwd": "${workspaceFolder}",
      "stopAtEntry": false,
      "internalConsoleOptions": "openOnSessionStart",
      "launchBrowser": {
        "enabled": true,
        "args": "${auto-detect-url}",
        "windows": {
          "command": "cmd.exe",
          "args": "/C start ${auto-detect-url}"
        },
        "osx": {
          "command": "open"
        },
        "linux": {
          "command": "xdg-open"
        }
      },
      "env": {
        "ASPNETCORE_ENVIRONMENT": "Development"
      },
      "sourceFileMap": {
        "/Views": "${workspaceFolder}/Views"
      }
    },
    {
      "name": ".NET Core Attach",
      "type": "coreclr",
      "request": "attach",
      "processId": "${command:pickProcess}"
    }
  ]
}