Your teacher certainly is focusing on fine details! Only a very careful reader looks at word-choices with such close scrutiny.
Regarding "fleeing" from imprisonment, I agree with your teacher. It is would be more accurate to write "escape from jail".
As for the second sentence, it is correct that we normally say "run away from home". But I don't agree that "flee from home" is necessarily wrong. It adds dramatic emphasis, and if that is your intent, then it's okay. For example, if she was running away from a particularly eggregious situation at home , "flee" would be an appropriate choice of verb. On the other hand, if she left home simply because she was wayward and rebellious, it wouldn't be as appropriate to use "flee".
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