I have managed to get a button to appear by adding this code to the FormViewDialog javascript function: 

options.buttons.splice(2, 0, {
    text: _t("Save & Duplicate"),
    classes: "btn-primary",
    click: function () {
    },
});

However i'm not sure what it is needed in the click function in order to get it to duplicate the current element and open the pop up form.

Edit: This is for odoo 12