In the UI it would be nice to duplicate the selected connection, in the menu "With Selected". 

The copy would be set with the same name plus some suffix (_copy, _1, whatever) and it is useful for when you have a connection with all equal fields except something in a particular one. 
airflow/www/views.py
"""Multiple delete."""
        self.datamodel.delete_all(items)
        self.update_redirect()
        return redirect(self.get_redirect())
    @action('varexport', 'Export', '', single=False)
    def action_varexport(self, items):
        """Export variables."""
        var_dict = {}
        decoder = json.JSONDecoder()
        for var in items:
            try:
                val = decoder.decode(var.val)
            except Exception:  
                val = var.val
            var_dict[var.key] = val
        response = make_response(json.dumps(var_dict, sort_keys=True, indent=4))
        response.headers["Content-Disposition"] = "attachment; filename=variables.json"
        response.headers["Content-Type"] = "application/json; charset=utf-8"
        return response
    @expose('/varimport', methods=["POST"])
    @action_logging
    def varimport(self):
        """Import variables"""
        try:
            variable_dict = json.loads(request.files['file'].read())
        except Exception:  
            self.update_redirect()
            flash("Missing file or syntax error.", 'error')
            return redirect(self.get_redirect())