Flexibility exercises for elbows and shoulders

Recently, I started to feel some pain after working out in my shoulders, wrists and right elbow so I am curious which are good warming up flexibility exercises for joints. I feel sometimes pain in elbow when I do muscle ups or too many pull-ups. 

This sounds more like the beginnings of tendonitis than mobility issues. You probably need to stretch but I don't think it will solve your problem. Rest is what you need, followed by progressively building up to pull ups rope climbs and muscle ups without pain. Pain is an indication you are doing too much or doing something beyond your strength level.