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
class DagRunModelView(AirflowModelView):
    """View to show records from DagRun table"""
    route_base = '/dagrun'
    datamodel = AirflowModelView.CustomSQLAInterface(models.DagRun)  
    class_permission_name = permissions.RESOURCE_DAG_RUN
    method_permission_name = {
        'add': 'create',
        'list': 'read',
        'action_clear': 'delete',
        'action_muldelete': 'delete',
        'action_set_running': 'edit',
        'action_set_failed': 'edit',
        'action_set_success': 'edit',
    }
    base_permissions = [
        permissions.ACTION_CAN_CREATE,
        permissions.ACTION_CAN_READ,
        permissions.ACTION_CAN_EDIT,
        permissions.ACTION_CAN_DELETE,
        permissions.ACTION_CAN_ACCESS_MENU,
    ]
    add_columns = ['state', 'dag_id', 'execution_date', 'run_id', 'external_trigger', 'conf']
    list_columns = [
        'state',
        'dag_id',
        'execution_date',
        'run_id',
        'run_type',
        'start_date',
        'end_date',