There's a few issue on Goering a 'successor'.
Although Goring was to be a successor in the Hitler's inner circle he this was far outside practical reality (say if he died). Hitler liked to keep everybody within his inner circle, armed forces and everything that he appointed under competition; Speer, Goebbels even Himmler were considered as potential candidates for succession. For example, before Speer was hospitalised during the war, he was well considered by many to be Hitler's successor until Goebbels and Goring plotted while he was sick. Speer being an individual who was largely responsible for running the war and somebody who Hitler admired in ways as an artist, somebody who was put in this position because of their sense of duty and a creative thinker. There were a number of candidates, but never a distinct second man.
Why would Goering be a candidate to Hitler? He was there since the beginning. He marched with Hitler in Munich, he supported him from the start, he made money for the party while providing connections with the German high society (being a the last wing Captain of the Red Baron's wing pilots) and was a great speaker. He was one of very few that Hitler trusted, felt comfortable and enjoyed a sense of camaraderie with. He also held a lot of power (which was important in Hitler's eyes), and being chief of the Luftwaffe was a natural choice.
sources: Inside the Third Reich - a. speer
Goering - r. mavrell & h. fraenkel
there's many more, but in my opinion those are the best ones.
Wasn't Doenitz first?