Karl Dönitz wasn't Hitlers successor. Hitler named him Reichspräsident. After Hindenburg died in 1934 Hitler united Reichskanzler (which he was) and Reichspräsident (which Hindenburg was). He transfered the powers of the Reichspräsident to himself with the "Law of the Head of State of the German Reich" which was approved by a referendum. After this Hitler called himself "Führer und Reichskanzler" and the Reichspräsident as an office and name disappered.

In his political will Hitler decided to split the offices of Reichspräsident and Reichskanzler again. He named Karl Dönitz Reichspräsident and Josef Goebbels Reichskanzler.

One day after Hitler killed himself Goebbles commited suicide with his wife and killed all of his children. Dönitz who was now Reichspräsident didn't name a new Reichskanzler.

I think those informations are important for your question.