'to get impatient' means to become impatient ,it refers to the sudden reaction at a certain moment 'to grow impatient' refers to the development of this emotion ( impatience) ,when it comes into existence gradually. It is a description of that feeling extended over a longer period of time in comparison to 'getting impatient' which is abrupt and sudden. "He gets impatient when waiting in a long line for tickets." "Don't get impatient ,you will find it soon." "He grew impatient waiting in the queue."

get impatient = to feel impatient now grow impatient= to feel impatience growing over a period of time