Flame trenches/deflectors are essential for avoiding reflections of acoustic waves from damaging the rocket system while taking off. This is discussed in this YouTube video - Why doesn't the sound of a rocket launch kill you?
But taking the artistic representation of Martian take off and landing, say from the movie Martian or Elon Musk's tweet, there is an absence of flame trench.
So this kindles the question - whether a flame trench is required in Martian condition. How will the launch site in Mars look like?