While they may be similar I don't think you can use them in every context.
Run - pass or cause to pass quickly or smoothly in a particular direction.
Run - move about in a hurried and hectic way.
There are multiple definitions for the word Ran but from my research these two most closely relate to flee. Also flee has more of a negative connotation to it for example.
Flee - run away from a place or situation of danger.
Flee - run away from (someone or something).
"I can't wait to run away and start my life in Europe!"
"I cant wait to flee and start my life in Europe!"
The second one doesn't sound right, even though both would need to defined more clearly with context clues, you can assume what the person who spoke the first sentence meant easier than the second.