Use Ctrl+K to clear the terminal.
But this is not possible in Linux Visual Studio Code.
For Linux you can do like below:
Via the command palette: ctrl+shift+p, "tclear"
To add this in shortcuts, copy paste this in keybinding file:
{
"key": "ctrl+k",
"command": "workbench.action.terminal.clear",
"when": "terminalFocus"
}