I think that whether it is ok to spend time with an old flame without your current partner being involved is very dependent on what type of relationship you are currently in.
I have a friend who is still very close to her ex husband, she invites him to dinner regularly and goes out to eat with him on weekends while her new husband is at work. At first I thought that this was a strange set up, but I found out that her current husband is perfectly ok with the situation and has become very good friends with his wife's ex.
I believe that the key to any successful relationship is trust and communication and as long as you are not sneaking around, it should be fine to maintain a friendship.
