I believe the scene in which Gatsby allows Daisy to quickly drive, hit Myrtle, and then flee the scene demonstrates recklessness in several ways.
1. Gatsby probably should not have let Daisy drive in the first place. The uncomfortable parting with Tom in New York before they jumped in the car likely had Daisy a little jittery to begin with, plus, being a rich woman, she probably had little road experience. She was angry, and driving like she was.
2. Myrtle only ran out to the car because she had been locked up by Wilson as he had discovered she was having an affair. In her effort to escape and be with Tom (because she thought Tom would be driving this car), Myrtle rushed to the car without caution knowing he would only slow enough to pick her up. Unfortunately this mistaken identity cost her life.
3. Any responsible human being in their rational mind would have stopped the car to determine how to help a situation like this. Gatsby encouraged her to stop, but Daisy was out of it and Gatsby let her be and drove on. Gatsby was too swayed by Daisy to do the right thing at the time.
Each of these reasons for recklessness demonstrate selfishness on behalf of the character whose flaws contributed to the reckless death.