the pile on a Flokati is about one and a half inches and it's a loose weave, so it would be a bit like trying to clean fringes with an extraction machine......
the only one I ever cleaned............I cheated...............took it to a friendly Dry Cleaner who had a very large machine for duvets
would never have contemplated using h/w/e...............this was some years ago, however and there might be newer designs with shorter pile and denser weave nowadays.