Walter White saved Pinkman many times on Breaking Bad and in the end Jesse only got free because of Walter. Then why didn't Jesse help him and left him there to die in the last episode?
Here's my take on it:
Walter wanted to die
He knew it was a matter of time until the police gets to him, and also he didn't have a lot of time left due to his illness. This is clear from the scene where he hands over the gun to Jesse and basically asks Jesse to shoot him.
Having realized that, Jesse avoids shooting Walter and says "do it yourself". He does so to spite Walter, and also because he's finally done with being bossed around by Walter. This is his small revenge for the harm Walter caused him.
Jesse Pinkman had two choices: either put someone new on his kill list (remember, he had some history) or just let Mister White die. In Walter's case, Jesse knew Walter had his cancer back and plus during the shooting got shot by his own gun machine (Jesse felt because Walt made some strange ouch noise in the shooting).
When Jesse says do it yourself, he knew Walter was harmed and (this is a hypothesis I am currently running) considering this, Walter gave Jesse a clear shoot oportunity to end his misery. From the beggining of the plan, Walter didn't plan to escape. He went to Skyler and told her about the plan. Hear it and there's no escape plan, just revenge and blood.
So, putting all this together, why would Jesse put one more on his kill list when this man is going to die (either by cancer or after he got shot) anyway sooner or later? And finally, Jesse was more interested in escape than killing someone else.