Well, leetcode doesn’t really like my answer but I think the overall approach is correct:

var flatten = function(head) {
    
    let list = head;
        
    while(list){
        if(list.child){
            // save the one that would have been next
            let temp = list.next;
            list.next = flatten(list.child);
            list.next.prev = temp;
                       
            // get to the end of our flattened list that
            // was appended and then add our original 'next'
            
            while(list.next){
                list = list.next
            }
            
            list.next = temp;
            temp.prev = list;
        }
         
        list = list.next;
        
    }
        
    return head
};